Attorney General Edwin Meese III, still searching for a candidate to head the Federal Bureau of Investigation, discussed the job yesterday with William W. Wilkins Jr., a federal appeals court judge from South Carolina, according to knowledgeable sources.

Wilkins, 45, who is being heavily promoted for the post by Sen. Strom Thurmond (R-S.C.), also serves as chairman of the U.S. Sentencing Commission, where his management style has come under strong criticism that would likely be aired if he were nominated as FBI director.

A senior White House official played down suggestions that Wilkins was the leading contender, saying that "we are considering a number of able candidates." He also expressed the White House's continuing irritation with Meese for allowing the FBI search to drag on for more than four months.

Wilkins' chances got a modest boost last week after President Reagan nominated Appeals Court Judge Robert H. Bork to the Supreme Court, disregarding Thurmond's advice that he pick a southerner to succeed Lewis F. Powell Jr. The White House then sent signals that it might appease Thurmond, who is ranking Republican on the Senate Judiciary Committee and a longtime administration stalwart, by tapping Wilkins, a former Thurmond aide.

Wilkins declined to be interviewed about his meeting with Meese.

The battle over Bork could further delay Judiciary Committee confirmation of any nominee to succeed former FBI director William H. Webster, now head of the Central Intelligence Agency. Sen. Dennis DeConcini (D-Ariz.), a committee member, is considered a long shot, but he has repeatedly criticized Meese's efforts on drug enforcement.

Justice Department spokesman Patrick Korten said Meese would have no comment and that he did not know whether Meese has interviewed other candidates for the FBI post.

While Wilkins was not initially viewed as a serious contender, that may have changed after several prominent candidates -- former deputy attorney general D. Lowell Jensen, Associate Attorney General Stephen S. Trott, Supreme Court Justice Byron R. White and former Pennsylvania governor Richard L. Thornburgh (R) -- declined to be considered for the 10-year appointment.

"We were informed early on that Judge Wilkins was a strong candidate for the position, that he was on the list of contenders," said Thurmond spokesman Mark Goodin. "Sen. Thurmond has received no direct indication that the situation has changed."

Since 1985, Wilkins has chaired the seven-member Sentencing Commission, created by Congress to make federal sentencing more uniform. The panel, which has been hampered by internal disputes and staffing problems, at first proposed sharply limiting judges' discretion in sentencing, then adopted a last-minute rewrite called "Draft X" that allowed judges far more latitude. The commission met its April 13 deadline when three other members drafted the revised version and persuaded Wilkins to go along.

One source close to the commission said Wilkins' appointment "would be an unmitigated disaster. The man cannot manage. He can't administer the commission, never mind the FBI."

Another commission official who declined to be named said that Wilkins "does not have any independent set of principles of his own. He sees every situation as a political opportunity. That's why the commission was wildly lurching from one extreme to another."

But Commissioner Michael K. Block said Wilkins would be a good choice and should not be blamed for any management problems. "He's an extremely capable person," Block said. "He's smart and he knows how to get things done."

Wilkins, a former South Carolina prosecutor and one-time law clerk for Appeals Court Judge Clement F. Haynsworth Jr., was named by Reagan to the U.S. District Court in 1981 and to the 4th U.S. Circuit Court of Appeals in Richmond last year.