In a private office several weeks ago, FBI agents showed up to question a banker who does business with the District of Columbia government.

Did the banker know of any payoffs to city officials, the agents asked. Had he been pressured to hire former city officials? Had he made illegal campaign contributions to Mayor Marion Barry?

According to the banker, he answered no to each question, and then posed his own: " 'Hey, when are you going to get the big guy?' "

He didn't get an answer, but among those familiar with U.S. Attorney Joseph E. diGenova's investigation of alleged corruption in the District government, the best guess is not soon, and maybe never.

The U.S. attorney's office and the FBI, which have kept Barry under scrutiny for at least four years, have intensified their inquiry as the result of recent information developed through an undercover FBI operation. But sources say prosecutors do not now have sufficient evidence to seek an indictment against Barry and are uncertain whether they ever will.

Investigators inside and outside the grand jury room are asking contractors, city officials and associates of Barry whether the mayor has used his official expense accounts for personal bills; manipulated the award of city contracts; accepted illegal campaign contributions; used cocaine, or directed payments to convicted cocaine dealer Karen K. Johnson in return for her refusal to testify before a federal grand jury.

They have reviewed the mayor's bank accounts, income tax forms and credit card expenditures, looked for evidence of offshore bank accounts and subpoenaed two pairs of shoes Barry received from a city contractor.

The public perception that the mayor is the ultimate object of the probe has deepened since the disclosure in May of a 17-month undercover FBI "sting" operation into city contracting, which set off more than four months of almost daily newspaper and television publicity.

Though diGenova has never mentioned Barry in any of his public statements, his highly publicized remarks about widespread and blatant corruption in the city government have fed speculation that the mayor must be involved.

The corruption convictions of 11 former or current Barry administration officials -- including two deputy mayors -- have also contributed to the perception.

At the January 1986 sentencing of former deputy mayor Ivanhoe Donaldson on charges of stealing $190,000 from the city, diGenova decried "raw corruption" in the city government. When a D.C. Lottery official was convicted of accepting an illegal gratuity, diGenova warned that "the days of wheeling, dealing and stealing in the D.C. government are over," and predicted more indictments.

His statements, along with the time lapse since the FBI ended the undercover phase of its investigation into city contracts, have created some public pressure on diGenova to show his hand or give up.

Federal prosecutors in other jurisdictions, including U.S. Attorney Rudolph A. Giuliani in New York, say investigations of public corruption are typically drawn-out affairs. "They are very, very difficult . . . . It's like going over a mountain," he said.

Sources said the prosecutors in diGenova's office have settled in for the long haul, though some indictments are expected in the next two to four months. One source said the prosecutors may be working on the investigation after their boss has moved on. DiGenova's term as U.S. attorney officially ends in December, though it could be extended.

Clendon Lee, a spokesman for diGenova, said last week that "the investigation is proceeding in an orderly fashion, with all appropriate resources applied to it and with every effort to resolve the matter as quickly as possible."

The investigators' interest in Barry appears to be divided into three main areas:The alleged payment of hush money to Johnson, as detailed by her in interviews with prosecutors and supported by FBI wiretaps and surveillance.

According to sources, Johnson told prosecutors that she sold Barry cocaine on 20 to 30 occasions between the fall of 1981 and late 1982, and that she received about $20,000 in exchange for her refusal to testify about the alleged sales before a federal grand jury four years ago.

Barry testified before the grand jury in 1984 that he never bought cocaine from Johnson, sources said, but they said prosecutors have no interest in trying to prove that Barry lied to make an isolated perjury case against him.

Such a case would pit the word of a convicted cocaine dealer, who has received immunity, against that of the mayor. Plus, sources said prosecutors believe that a perjury charge in this situation might seem petty to a jury.

The prosecutors are more interested in whether Barry knew of or approved the alleged payments to Johnson. Barry has denied any knowledge of the alleged payments, and no evidence to the contrary has been disclosed.

At least two people may be able to address the question of Barry's knowledge: John A. Shorter, Johnson's former attorney, and D.C. contractor John B. Clyburn. Sources said Johnson has named both as participants in the alleged hush money scheme. Johnson has also said contractor Roy Littlejohn may have contributed funds.

All three men have denied wrongdoing through their attorneys. None has been charged.

The prosecutors have not yet tried to gain the cooperation of either Clyburn or Littlejohn, apparently because they are still trying to collect evidence with which to pressure them into cooperating, sources said.

It is unclear whether the U.S. attorney's office has sought Shorter's cooperation. But sources said the lawyer, now serving a sentence for tax evasion in an Alabama prison, has no intention of aiding the prosecutors. "He's a stand-up kind of guy," said a close friend of Shorter's. "He won't help them." Alleged misuse of the mayor's official accounts. Prosecutors have questioned numerous former and current city officials about whether Barry paid for personal goods or services out of funds set aside for his official expenses. Barry has denied misusing the funds.

In particular, prosecutors have asked about $5,750 in checks written out to cash from the mayor's ceremonial fund, as well as personal loans to city employes and the alleged payment of a $1,500 fur coat bill for the mayor's wife Effi from that account.

Both city officials who controlled the fund -- Robert Robinson, a former administrative aide to Barry, and Dwight S. Cropp, a top adviser to the mayor -- have testified before the grand jury.

Both have told associates that they do not believe the mayor converted official funds to his personal use. Robinson has told associates that the prosecutors are trying to "squeeze" him to link the mayor to illegality, but that to his knowledge, the mayor did not personally benefit from the use of official funds.

In an account provided to city officials, Robinson said he decided on his own to use money from the ceremonial fund to pay Effi Barry's fur coat bill to save the mayor from public embarrassment when a local furrier complained, sources said. The sources said Robinson also told city officials that Barry did not know of his action.

Barry has said that he only learned that Robinson paid the bill from the furrier and that he repaid Robinson in cash. Barry said Robinson told him he paid the bill out of his own pocket.

Contract awards. Investigators are trying to determine whether Barry improperly influenced contract awards or obtained benefits from contractors as part of a wide-ranging investigation of numerous city officials and contractors. Barry has said repeatedly that he has never "steered" contracts.

Prosecutors are exploring whether they can show a pattern of illegal activity by a group of people that would fall under the federal Racketeer Influenced and Corrupt Organization (RICO) statute and conspiracy and extortion laws.

One source said investigators are uncertain whether the theory of a broad conspiracy to defraud the city government will pan out or whether they will be left with separate prosecutions of individual District officials and contractors.

The FBI's "sting" operation is believed to have produced evidence of illegal activity by a number of individuals, including David E. Rivers, former secretary of the District; Clyburn, and T. Conrad Monts, a local developer. All have denied wrongdoing and no charges have been filed.

In recent weeks, sources said FBI agents and prosecutors have turned their attention to Barry's selection of investment banking firms to handle the city's bond sales. Barry has said that in making his choices, he relies entirely on the advice of a private firm under contract to provide financial advice.

Sources said prosecutors were unable to develop evidence against Barry during investigations of two former deputy mayors, Ivanhoe Donaldson and Alphonse G. Hill, both of whom were convicted of defrauding the government.

Donaldson and Hill testified before federal grand juries after their convictions. Hill has told associates that he was not asked about Barry. The nature of the questioning of Donaldson, who has testified repeatedly, could not be determined.

White-collar crime experts say that to prove a conspiracy, it is not necessary to show that a public official personally directed business to selected firms. Evidence that an official knew of illegal contract awards or allowed corrupt contracting practices to flourish could be sufficient, they said, if there is evidence that the official received substantial benefits -- money or gifts from favored contractors.

Sources said IRS agents have examined Barry's financial records in an attempt to determine whether he had improperly received any income, but found nothing they considered significant.

Sources said that one former District official, Jose Gutierrez, has told FBI agents that Barry personally told him whom to pick as contractors and subcontractors while Gutierrez headed the city's Department of Administrative Services, the city's main purchasing agency. But Gutierrez provided no evidence of payoffs of any type to Barry, the sources said.

Gutierrez was criticized by a U.S. District Court judge for circumventing city purchasing regulations in awarding a city lease to a firm headed by a friend. Barry fired Gutierrez after an internal report accused him of steering contracts.

DiGenova's interest in using the RICO statute leads some observers to compare the inquiry to the prosecution of Maryland governor Marvin Mandel in the mid-1970s and the investigation of Detroit city officials three years ago, though Justice Department sources say the District probe is much broader than either.

Mandel was sentenced to four years in prison in 1977 for accepting $350,000 in gifts and financial assistance from a group of race track owners while using his official position to enrich their race track business. He was convicted of one count of violating the RICO statute and 17 counts of mail fraud.

Since Mandel's conviction, the RICO act has become increasingly popular in public corruption cases because it gives prosecutors greater flexibility in the use of evidence as proof of a "pattern" of illegal activity. A RICO case can be brought on the basis of two federal criminal violations within 10 years.

Federal prosecutors were able to obtain a conviction for racketeering and mail fraud against Mandel although they were never able to link directly the gifts and financial assistance that he received with his efforts to help the race track owners.

In the Detroit case, the FBI persuaded a partner in a sludge treatment firm headed by a friend of Mayor Coleman Young to secretly tape conversations with his partners, and later obtained court authorization for wiretaps. Based almost entirely on the tapes, a jury convicted Charles Beckman, the city's water director, of taking kickbacks.

Young, whose town house was wiretapped, was never charged. Prosecutors sought to name Young as an unindicted coconspirator, but a judge turned down their request due to lack of evidence.

The case involved 75 FBI agents and 6,000 hours of secretly recorded conversations. Nearly a year passed between the end of the undercover operation and indictments, while prosecutors assembled the evidence and interviewed witnesses.