If the present timetable is met, the president would make a nomination sometime in the next 10 days to replace Justice Byron R. White, who is retiring in June, according to sources who have been working in the process or aiding it from the outside.
Among the names being circulated by those sources are two Southern lawyers: former Virginia Gov. Gerald L. Baliles and former American Bar Association President Talbot S. D'Alemberte of Miami.
The nomination must be settled in a matter of days to avoid having the Senate confirmation process run well into September. If Mr. Clinton delays much longer, the court will be down to eight justices when it returns in October.
At this point, those involved in the search say the focus has turned from women to men and from sitting judges to lawyers in private practice with public service backgrounds.
It is hard to monitor the process from outside the White House because the reports of these switches may reflect more of an attempt to satisfy a political constituency than a sincere reflection of what the president wants.
The switch in emphasis has raised concerns because it suggests that the administration is trying to satisfy some political constituency rather than reflect the president's personal inclinations.
A private adviser who has been asked to help in the process, speaking on condition of anonymity, said yesterday that Mr. Clinton seems to be leaning toward a surprise choice -- someone whose name has not figured prominently in the speculation.
Mr. Baliles is now an attorney in the former Richmond firm of retired Supreme Court Justice Lewis F. Powell Jr. He is believed to be emerging as a strong candidate should Mr. Clinton settle on a private lawyer who has had a public career -- especially if the president wants to choose someone from the South, as some insiders suggest.
Mr. Baliles is a former state attorney general and legislator in Virginia. He was considered for the U.S. attorney general's job before Mr. Clinton chose Miami prosecutor Janet Reno. The former Virginia governor has a number of characteristics the president is believed to favor in a nominee: He is under 60 years of age (he will be 53 in July), is a moderate Democrat, and has shown he can work at building a consensus on tough issues.
Another Southern attorney who has some support -- although it is not clear that he is on the president's preferred list -- is Mr. D'Alemberte, a former Florida legislator who has just turned 60 and is well-known to the attorney general. Mr. D'Alemberte, who recently served as the American Bar Association president and is a former teacher of law, was a partner in a firm with Ms. Reno in Miami some years ago before she became a prosecutor.
Ms. Reno is among a handful of advisers working with the president on the nomination, according to the sources. The others are first lady Hillary Rodham Clinton and two of the president's key staff lawyers -- Bernard Nussbaum and Ronald Klain.
Among judges who have been getting strong consideration in the later rounds of review is U.S. Circuit Judge Stephen H. Breyer, 54, of Cambridge, Mass., who is a "really serious candidate," according to one Capitol Hill source. A moderate in his views, Mr. Breyer reportedly has sound personal alliances with Republican members of the Senate Judiciary Committee, even though he is a former aide to liberal Democratic Sen. Edward M. Kennedy of Massachusetts.