A federal judge from South Carolina withdrew from consideration to head the Federal Bureau of Investigation yesterday amid conflicting reports on whether he was close to being offered the job.

A senior White House official said President Reagan never reached the point of authorizing that the FBI post be offered to Appeals Court Judge William W. Wilkins Jr. Other administration sources said Wilkins bowed out because he was unlikely to be nominated, in part because his tenure as chairman of the U.S. Sentencing Commission was attracting widespread criticism.

But Sen. Strom Thurmond (R-S.C.), who heavily promoted Wilkins, one of his former legislative aides, said yesterday he is certain that Reagan would have nominated Wilkins. "We received no indication that Judge Wilkins was anything but the leading candidate for the FBI," Thurmond spokesman Mark Goodin said.

Instead, sources said, Reagan wanted to offer Thurmond a consolation prize after the senator had pushed Wilkins hard for the Supreme Court. When Reagan nominated Appeals Court Judge Robert H. Bork, Thurmond, ranking Republican on the Senate Judiciary Committee, signaled his disappointment by issuing a lukewarm statement that he would "expect to support Judge Bork" but wished a southerner had been chosen.

Attorney General Edwin Meese III interviewed Wilkins Wednesday at the behest of the White House, sources said, but the attorney general never favored Wilkins for the job.

"Strom was beating the drums as loud as he could," the White House official said. He said White House chief of staff Howard H. Baker Jr. was "trying to keep Strom happy," but that Thurmond "got way out in front" on the possible FBI nomination.

A Republican source said the administration is playing down Wilkins' candidacy because "the White House wants to save Ed Meese the embarrassment of having another person turn down the job."

Wilkins, 45, a former prosecutor, said in a statement: "After careful reflection and a great deal of thought, I have decided to withdraw my name from consideration. . . . I am deeply honored to have been considered for this important position. However, family considerations and my strong desire to continue to serve on the federal judiciary have led me to make this decision."

Wilkins, who has two college-age children, would have had to take a significant pay cut by giving up an outside teaching position to take the $89,000-a-year FBI job, the Republican source said.

A Democratic source called the speculation about Wilkins "a trial balloon" that quickly burst when several Sentencing Commission officials criticized Wilkins as an inept manager who had lost control over the panel's direction. The commission, created by Congress in 1984 to make criminal sentencing more uniform, was hampered by internal disputes and staffing problems.

The White House official expressed renewed "impatience" with Meese for allowing the FBI search to drag on since early March, when William H. Webster was nominated to head the Central Intelligence Agency. Assistant FBI Director John Otto has been running the bureau since Webster's confirmation.

Sources said some potential candidates appear reluctant to take on the 10-year appointment. 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 have all withdrawn from consideration.