J. Harvie Wilkinson III, a 38-year-old Republican law professor serving in the Justice Department's civil rights division, is expected to be nominated to fill a vacancy on the U.S. 4th Circuit Court of Appeals in Richmond.

Sen. John W. Warner (R-Va.) said yesterday that the White House is considering Wilkinson for the post, which has become a source of tension between the Reagan administration and Republicans in Virginia's congressional delegation.

Warner, backed by the delegation and the Virginia State Bar, had urged the appointment of one of three U.S. District Court judges now sitting in Virginia--Albert V. Bryan Jr., 56, of Alexandria; J. Calvitt Clarke Jr., 62, of Norfolk, and Glen M. Williams, 62, of Abingdon in Southwest Virginia. Warner said in a statement that he called his candidates yesterday and thanked them for offering their names, a move that was seen as a clear indication that the competition for the job is over.

In the statement, Warner praised Wilkinson's "legal, literary and academic" achievements, but noted that he had held out for a nominee with experience in trial practice and service on the bench.

"I never deviated from that position throughout the long consultations with the senior presidential advisers," the senator said.

Warner said yesterday that Attorney General William French Smith and other administration officials had indicated they wanted to fill the appeals court seat with someone who "by virtue of age could serve 15 to 20 years" before retirement, which would rule out all of Warner's candidates.

Virginia's senior senator also noted that by tradition the president has the final word on nominees to appellate courts, who must be confirmed by the Senate, while senators of the president's party can block district court appointments through the practice known as senatorial courtesy.

A White House spokesman said yesterday that no final decision has been made on the 4th Circuit nominee, although it appeared Wilkinson's nomination awaits only the outcome of an FBI background check. Wilkinson declined comment yesterday.

Wilkinson, a former editor of The Virginian-Pilot in Norfolk and author of books on Virginia politics, the Supreme Court and school desegregation, is on leave from his job as a professor of law at the University of Virginia. Regarded as a conservative, Wilkinson's practical political experience included campaign work for Gov. Linwood Holton, the moderate Republican elected in 1969, and his own unsuccessful campaign for Congress in the Richmond-based 3rd District.

At the Justice Department, Wilkinson has helped draft some of the cases allowing reconsideration of busing plans to achieve school desegration, a position that has helped fuel criticism of the Reagan administration's stand on civil rights.

In choosing Wilkinson, the White House avoided one complaint raised last spring when Kenneth Starr, a 36-year-old Californian and top aide to Attorney General Smith, was considered a leading candidate for the 4th circuit vacancy. Republicans in the state delegation considered the nomination of non-Virginian as an affront, because the seat was being vacated by a Virginian, John D. Butzner of Richmond.

Starr was appointed to the U.S. Court of Appeals in Washington and Warner issued a statement saying his views had been "taken into consideration" on the matter of the 4th Circuit vacancy. Yesterday, some Republicans described Wilkinson as "a compromise candidate."

"At least, Wilkinson's a Virginian," a spokesman for Rep. Stan Parris (R-Va.) said yesterday. "That was a concern that all members of the delegation had."

James C. Roberts, a past president of the Virginia State Bar, said it was Starr's legal experience, as much as his lack of Virginia credentials, that had concerned lawyers in the state. "I think the same lacking is present here," said Roberts, commenting on Wilkinson.