Even as President Reagan vowed to stand by Robert H. Bork and force a Senate vote on his nomination to the Supreme Court, Justice Department and White House officials have started to consider who they will pick next to fill the high court vacancy.

Among those most frequently mentioned are federal appeals court judges Patrick E. Higginbotham of Dallas, J. Clifford Wallace of San Diego, Pasco M. Bowman of Kansas City and Roger Miner of New York.

Frank Easterbrook and Richard Posner, federal appeals court judges in Chicago, are cited as possible nominees but are considered controversial choices whose selection would ensure another fierce confirmation struggle. Other possibilities include federal appeals court judges Anthony M. Kennedy of Sacramento, Calif., and Thomas G. Gee of Austin, Tex.

Sources said Justice Department lawyers have started to prepare background material on possible choices whose records have not been exhaustively researched. If Bork is defeated or his nomination withdrawn, the sources said, Reagan wants to act within days to fill the vacancy.

Sen. Orrin G. Hatch (R-Utah), a leading conservative who might otherwise be an attractive nominee, faces a problem because the Senate passed a pay raise for federal judges and a constitutional provision would bar his being named to the court unless Congress passed a special law reducing the salary for his seat.

Southern senators have been pushing hard for Higginbotham, 48, an Alabama native named to the federal trial court in Dallas by President Gerald R. Ford and promoted to the appeals court in 1982. Administration sources say his chances have dimmed because the administration, which relied unsuccessfully on conservative southern Democrats to support Bork, is reluctant to reward them by choosing a southerner.

"Right-to-life" groups have also expressed concern about Higginbotham, who last year wrote a decision striking down a Louisiana law that barred experimentation with fetal remains and required doctors, within 24 hours of performing an abortion, to inform the patient "personally" of her right to have the fetus cremated, buried or disposed of as waste tissue.

However, he went out of his way to note that the Supreme Court's abortion rulings "have been vigorously attacked" by legal scholars and justices themselves and also upheld a Texas law making homosexual sodomy illegal. Conservatives have criticized his rulings in search-and-seizure cases.

Wallace, 58, a judge on the 9th U.S. Circuit Court of Appeals since 1972, and a federal trial court judge for two years previously, is known as an ardent advocate of judicial restraint.

A devout Mormon, he has said the Bible provides "great scriptural support for the death penalty," questioned the need for "a wall between state and religion" and warned, "I don't think the Constitution was developed to answer all questions or cure all social ills."

Bowman, 53, a former law school dean, was appointed to the 8th U.S. Circuit Court of Appeals in 1983. An authority on business and commercial law, he dissented from a decision dismissing a $10 million libel suit by then-South Dakota Gov. William J. Janklow, upheld a Missouri Highway Patrol mandatory-retirement age of 60 and disagreed with a ruling upholding a St. Louis school desegregation plan. He said the state could not be required to fund a remedy broader than the proven constitutional violation.

Miner, 53, was named to the federal trial bench by Reagan in 1981 and promoted to the appeals court in 1985.

In a 1984 review of judges picked by Reagan, the conservative publication Benchmark said that "when called upon to exercise judicial discretion," Miner "almost always proved himself the type of judge President Reagan had pledged to appoint." The review criticized him for a 1982 ruling that a body-cavity search of a corrections officer may have violated his constitutional rights.

In 1984, he refused to appoint a legal guardian for the severely handicapped Baby Jane Doe, whose parents rejected possibly life-extending surgery.