White House counsel Fred Fielding was asked explicitly by the FBI last year whether he saw any need to question Secretary of Labor-designate Raymond J. Donovan about alleged social contacts with gangland figures, and said he did not, FBI Director William H. Webster reported yesterday.

Webster said the question was raised with Fielding, who was President-elect Reagan's conflict-of-interest adviser at the time, on Jan. 11, 1981. The Senate Labor Committee began confirmation hearings on Donovan's Cabinet appointment the next day.

The question was, "Do you want us to do any more and he Fielding didn't think it was necessary," Webster said at a lengthy press conference in which he defended the FBI's work in the Donovan case despite the shortcomings that have since come to light.

"I don't consider this a bungled investigation," Webster said. "Sure, we made some mistakes in handling paper but I've taken steps to correct that."

Senate Labor Committee Chairman Orrin G. Hatch (R-Utah) expressed a different view, promising a formal investigation of the FBI's performance before Donovan's confirmation by the Senate on Feb. 3, 1981.

Hatch said he also intends to ask Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.) to hold up the nomination of Francis B. Mullen as head of the Drug Enforcement Administration until questions about the Donovan case "are fully resolved."

Mullen, who is still one of the FBI's executive assistant directors as well as acting DEA administrator, was in charge of the Donovan inquiry.

In an interview last week, Mullen said he made the decision not to tell the Senate Labor Committee during the confirmation process about an extensive wiretap of organized crime figures during which Donovan's name was mentioned in a social context.

Mullen contended that the conversation, between William P. Masselli, a reputed Mafia "soldier," and his son, Nat, was "not pertinent" to the bureau's inquiry into Donovan's qualifications.

At his press conference yesterday, Webster emphasized that President Reagan's transition team was told of the tape-recorded conversation along with several other items, including an informant's report that Donovan had gone to the 1979 Super Bowl in Miami with Masselli and other Mafia figures.

The FBI director took the position that this was sufficient.

"I don't make any claim to perfection," Webster said of the Donovan background investigation, "but it was not an attempt to conceal" anything. He said the FBI's traditional role in making such checks is to keep the incoming president and his aides informed, and not the Senate committees that hold confirmation hearings on the nominations. "The FBI has not been the investigative arm of the Senate in the past," Webster said.

Fielding told The Washington Post last week that he did remember speaking with Anthony Adamski, the FBI official immediately in charge of the Donovan inquiry, on Jan. 11, 1981, and being told of both of the alleged Super Bowl trip and of a separate report linking Donovan's name to "hoodlums." He did not dispute that he had been told the second report came from "a tape recording." But he said it did not dawn on him that Adamski was talking about a wiretap and it was clear he did not ask.

Webster said Adamski summarized the conversation the next day in an internal FBI memo. According to FBI executive assistant director John Otto, Adamski reported having asked Fielding, "Should we go ahead and interview Mr. Donovan? and the reply was, 'Not at this time.' "

It was not clear whether Adamski conveyed the information with any sense of urgency or whether Fielding had been supplied with any other information concerning Masselli, a reputed member of the Genovese family of the Mafia.

But a federal grand jury at the time was investigating whether there was any fraud involved in his formation of a trucking company as a minority business enterprise and its role as a multimillion-dollar subcontactor for Donovan's firm, the Schiavone Construction Co. The FBI has also acknowledged that Donovan probably knew of reports at the time that Masselli had "muscled" aside another company to establish himself as a Schiavone subcontractor. The target of an extensive organized crime wiretap in 1979, Masselli had no previous experience in the trucking and excavation business.

Fielding was reported to be suffering from a strep throat yesterday and "barely able to talk" but he approved a 1 1/2-page statement reiterating much of what he said last week.

In the statement, Fielding said Adamski "did not express serious concern about the information." Fielding said he indicated to the agent that "little purpose would be served by interviewing Mr. Donovan at the time, given the absence of confirming facts or any suggestion of criminal wrongdoing, but that the future course of the investigation was a matter for the FBI to determine."

Fielding said the FBI did not tell the White House about "the existence of the so-called 'Masselli wiretaps' " either, but "it is apparent now that some information derived from such a wiretap was conveyed in a general sense, without identification of its source, both to the White House and the Senate committee in January, 1981."

According to informed sources, more information about Masselli's relationships with Donovan's company and references to "Ray" can be gleaned from the hundreds of hours of tapes compiled during the 1979 wiretap. But these went unexplored until special prosecutor Leon Silverman began investigating unresolved allegations about the labor secretary this year.

Hatch did ask Mullen at a Jan. 27, 1981, hearing about organized crime wiretaps in general whether it was "correct to say you found absolutely nothing pertaining to Schiavone Construction" on them.

Mullen replied, "That is correct, senator. We located no reference to Mr. Donovan or Schiavone Construction Co."

Mullen said in last week's interview that he was mentally limiting his response to organized crime wiretaps in New Jersey. The Masselli tap was carried out in New York.

Webster also said the FBI's background checks are frequently hurried investigations and constitute no more than "a best effort kind of product" under tight deadlines.

If the FBI is to be "the certifier of someone's reputation," he said, that "has to be made more clear to us" and the bureau will need to devote considerably more time and money to the task.

Hatch said his committee's investigation would begin once Silverman has concluded his work.