William M. Isaac, who guided the Federal Deposit Insurance Corp. through the most difficult period in its 51-year history, has told the White House that he does not want to be reappointed chairman and would like to depart the board by May or June, sources said.

Isaac has gained enormous respect throughout the banking industry and Congress for his handling of the agency during a period of record bank failures, including last summer's collapse of Continental Illinois National Bank, then the nation's eighth-largest.

Until 1981 -- when the banking industry was strained by back-to-back recessions, increasing competition from non-bank financial companies, deregulation of interest rates and the Latin American debt crisis -- the FDIC was a sleepy agency that handled a few bank failures each year and insured deposits in most U.S. banks.

As a result, appointees to the FDIC were often picked as much for their political leanings as for their expertise in banking, industry sources said. Bankers say that times have changed, and are strenuously lobbying to make sure that Isaac's successor has broad banking expertise.

"It is not a time for amateur hour," said Gerald Lowrie, director of government relations for the American Bankers Association. Lowrie said that if the White House looks to Isaac's successor more "to satisfy political interests" than to find the best available candidate, "it will be one of the more significant mistakes they could make."

Administration sources said Treasury Secretary Donald T. Regan is convinced that politics must take second place to qualifications in the search for a successor, and that the Treasury is playing the major role in trying to find the replacement.

The FDIC insures deposits up to $100,000 at most banks. It also regulates about 9,000 state-chartered banks that are not members of the Federal Reserve system, and it is the receiver in most bank failures.

Among the names proposed to the Treasury by banking industry officials are Philip F. Searle, chairman of Sun Banks in Florida; Dennis W. Dunne, former president of Norwest Corp.'s Duluth bank; William Rue, vice chairman of First Kentucky, and Charles Lord, now with the securities firm Prudential-Bache and once an acting comptroller of the currency.

Searle, the only one of the three bankers who could be reached, said he was aware his name was on a list, but said he knows little more than that.

Others who have either been considered by the White House or who have indicated their interest in the job include John Rousselot, the former Republican congressman from California; Roger Mehle, former assistant secretary of the Treasury; Richard Breeden, executive director of Vice President Bush's commission on reform of the financial system, and Richard Heldridge, a director of the Export-Import Bank.

Heldridge was the White House's choice to become FDIC chairman last February, when Isaac's six-year term as a member of the FDIC board expired. Sources said the White House preferred Heldridge because he was more closely aligned with the Reagan administration and had banking experience. Isaac was appointed to the FDIC board in 1978 by President Carter and became chairman in 1981.

But the Senate Republican leadership -- including Banking Committee Chairman Jake Garn (R-Utah) and Majority Leader Howard Baker (R-Tenn.) -- told the White House last spring they would not hold hearings on a nominee, unless it was Isaac. The law permitted Isaac to serve as chairman until the Senate confirmed a successor.

Last February, Isaac wanted to be reappointed, sources said, although he told the White House he would vacate the post after the election. Isaac reportedly was concerned that it would be difficult to find a top-quality person for the job until after the election and felt he should stay around to help guide new banking legislation through Congress. The legislation was never approved.

By last fall, Treasury sources said, the White House was ready to renominate Isaac as soon as the election was over. Isaac, however, recently told the administration he no longer wants the nomination, but will serve until a successor is found.