Five Chicago aldermen close to Mayor Harold Washington, a prominent Cook County officeholder with huge patronage powers and several lesser city officials have been linked to the latest undercover probe by federal authorities of Windy City political corruption.

Disclosures about the "sting" operation, which involved the FBI's use of a convicted swindler trying to buy favors, have shaken Washington's administration and cast a cloud over Circuit Court Clerk Morgan Finley, a political protege of the late mayor Richard J. (Boss) Daley.

Allegations of wrongdoing by Washington's appointees come at a crucial moment in the mayor's term. A federal judge recently approved the redistricting of seven city wards and set a special election for March 18 to choose aldermen.

The election could shift the balance of power in the 50-member City Council from the mayor's entrenched white opponents, who control 29 aldermen, to Washington. His 3-year-old administration has been crippled by the fact that he controls only 21 council votes.

The election results will be read as a harbinger of the 1987 mayoral race. Former mayor Jane Byrne has said she will oppose Washington in the Democratic primary 13 months hence.

At the same time, the investigation has raised questions about the methods -- and the man -- used by law enforcement officials hunting municipal corruption in the nation's third-largest city. These concerns center on Michael Raymond, who has served time in prison on various convictions and operated as an undercover informant though he reportedly was suspected of other crimes.

No indictments or criminal charges have been filed in what the press here has dubbed "The Mole" probe. But knowledgeable sources said they believe that as many as a dozen persons may be implicated in the investigation.

This sting comes in the aftermath of an extensive undercover investigation in the Circuit Court system that has led to the conviction of several judges and a credit-card sting aimed at businessmen who attempt to write off visits to suburban girlie bars as tax-deductible expenses.

Washington has fired two senior city employes for allegedly taking money from Raymond and has put others on leave. He also has launched an internal investigation.

Finley, 60, who has been court clerk since 1974 and whose domain encompasses hundreds of jobs dispensed as political patronage, has denied allegations, attributed in the local news media to unnamed sources, that he is connected to a $25,000 payoff from Raymond.

The undercover operation came to light shortly after Christmas, when several aldermen told local reporters that they were being questioned by FBI agents about their contacts with Raymond.

Raymond, 56, who testified under the alias "John White" about stock swindles before the Senate permanent subcommittee on investigations in 1971, spent 18 months here as an FBI informant. Working from a posh, bugged apartment, he posed as an official of a New York firm that was seeking lucrative city contracts to collect millions of dollars in unpaid parking tickets.

Raymond said he represented Systematic Recovery Services Inc. and sought to take over scofflaw collections from another firm, Datacom Systems Corp. of New Jersey. Both firms have competed for and won similar contracts in New York City.

Datacom employed Ivanhoe Donaldson, once one of District of Columbia Mayor Marion Barry's closest aides, as a part-time consultant while the firm was seeking business here. Probers are said to be interested in reviewing Datacom's contracts with Chicago. Donaldson pleaded guilty last month to stealing $190,000 from the D.C. government and covering up the wrongdoing.

New York City officials launched an investigation of such contracts last week after allegations of improprieties surfaced there. A New York parking official has been charged with accepting a $5,000 bribe.

Executives of both collection firms have denied all allegations of wrongdoing. Officials of Systematic Recovery Services have said they cooperated fully with the FBI operation here. A Datacom executive has said his firm will cooperate fully with the federal investigation.

Although the FBI and the U.S. Attorney's office have refused to comment on details of the Chicago sting, news media here have reported that Raymond used an apartment in the plush Lake Point Towers as his base and lavishly wined and dined city officials at restaurants around town. He apparently carried concealed electronics gear to record his conversations.

The FBI also reportedly eavesdropped on Raymond's apartment from a neighboring unit and "phoned in plays" to him during his conversations with officials.

Raymond's whereabouts are unknown. He apparently has been in the federal Witness Protection Program for several years, but the Chicago Tribune, the Chicago Sun-Times and the magazine Miami/Florida South have reported that several law enforcement agencies in Florida have sought Raymond for questioning in connection with the separate disappearances of three people during the 1970s.

The five aldermen linked to Raymond deny wrongdoing. The aldermen, all of them black, are members of the mayor's embattled bloc of 21 votes on the council. The fact that the early disclosures centered on Washington's allies or appointees stirred many of the mayor's supporters.

"The mayor's handled it well," said Alderman Danny K. Davis, in a comment typical of Washington's allies. "He's demonstrated toughness in weeding out corruption."

Washington's opponents have had little to say. "I've kept my mouth shut. I think I should stand by the sidelines," said Alderman Edward Burke, one of the mayor's most persistent critics.