After time for reflection following her unsuccessful bid for the Senate earlier this month, Rep. Lynn Martin (R-Ill.) has told the White House that she is interested in becoming labor secretary.

Administration sources said Martin spoke to President Bush and White House Chief of Staff John H. Sununu last Thursday and told them she was interested in succeeding Elizabeth Hanford Dole in the Cabinet post. Dole leaves office today.

The decision appears to make the secretary's job a two-woman race. Until Martin tossed her hat into the ring, the front-runner for the labor job appeared to be Constance B. Newman, director of the Office of Personnel Management. Newman is one of the highest-ranking black women in the Bush administration and supporters argue that her appointment to the Cabinet would remove some of the political sting from Bush's veto of the civil rights bill this year.

Sources said yesterday it was unclear which way the White House might be leaning or when a decision would be made.

Martin, a five-term member of Congress and Bush ally, had talked with White House officials immediately after her loss to Sen. Paul Simon (D-Ill.) and indicated she wasn't sure she was interested in the labor post. She was told to take her time because there would be other openings coming up.

Since then, however, two of those openings have been filled. William J. Bennett, the national drug policy director, has been chosen by Bush to head the Republican National Committee, and Florida Gov. Bob Martinez, who was defeated in his bid for reelection, has been picked to replace Bennett.

Martin was unavailable for comment yesterday. She is in Oman as a representative of the president on a ceremonial mission and won't return to Washington until later this week.