The White House is moving quickly to find a successor to Labor Secretary Raymond J. Donovan, and two leading candidates are Federal Trade Commission Chairman James C. Miller III and White House political adviser Edward J. Rollins, officials said yesterday.

U.S. Trade Representative William E. Brock is also considered a major contender for the job, but Republican political sources indicated yesterday that he is not interested.

Miller was reported to have the backing of White House deputy chief of staff Michael K. Deaver, while Rollins was said to be backed by Vice President Bush, Sen. Paul Laxalt (R-Nev.) and Senate Labor and Human Resources Committee Chairman Orrin G. Hatch (R-Utah.)

Officials said Reagan is expected to decide on a successor before his nationally televised news conference scheduled Thursday night.

Miller has been at the forefront of administration deregulation efforts. He was executive director of the vice president's Task Force on Regulatory Relief in 1981 and, since becoming FTC chairman in 1981, has aggressively pushed to relax regulations on industry and business.

Rollins has been a Reagan political adviser since early in the president's first administration and has been instrumental in Reagan's campaign strategy of seeking rank-and-file blue-collar support. He was director of the Reagan-Bush committee last year.

Rollins had expressed interest in the post. He worked as a political consultant immediately after Reagan's election but then returned to the White House as a top assistant to chief of staff Donald T. Regan when it appeared that the Labor post might not be open for a while.

Miller and Rollins are known to be interested in the job now.

Brock, a former Tennessee senator and Republican Party chairman, has been Reagan's chief trade negotiator since the beginning of Reagan's first term. A GOP moderate, Brock clashed with conservatives during the 1980 campaign, but he has earned respect in the White House for his handling of troublesome trade issues.

Brock currently holds Cabinet rank.

Donovan resigned last week after a New York State Supreme Court judge ruled that he must stand trial on 137 counts of grand larceny and fraud.

Although Reagan has consistently done well among blue-collar workers, Donovan was criticized inside and outside the administration for lack of contact with leaders of organized labor.

This has led some White House officials to conclude that Reagan wants a second-term labor secretary who can build bridges to the labor movement, even if its leaders remain critics of administration policy. Rollins and Brock appear to be capable of making contact with labor leaders.

At the same time, the White House is not expected to reverse the basic course set in Reagan's first term of cutting the federal budget and relaxing regulations at the Labor Department.

Miller's record at the FTC and at the Office of Management and Budget, where he was an assistant to Director David A. Stockman in 1981, would appear to fit this pattern.

Officials said other possible nominees include Rep. Matthew J. Rinaldo (R-N.J.) and White House officials Lee Verstandig and John A. Svahn.