Former D.C. City Council Chairman Sterling Tucker and former Arlington County Board Chairman Joseph S. Wholey are among the leading candidates to become general manager of the controversy-ridden Metro transit authority, according to reliable sources.

Tucker, now a private consultant, and Wholey, a university professor who also heads a consulting firm, are the two most prominent political figures under consideration by Metro's board of directors for the powerful general manager's post. Richard S. Page, Metro's current general manager, has announced plans to resign May 31.

In the past week, the Metro board's search for a successor to Page was reported to have narrowed to five main contenders. They included two senior Metro administrators--William A. Boleyn, the assistant general manager for finance and comptroller, and Theodore G. Weigle, assistant general manager for transit operations. Also under consideration, sources said, was M. L. Clark Tyler, Amtrak's group vice president for passenger services and communications.

The often contentious Metro board, which includes politicians from the District, Northern Virginia and suburban Maryland, was described yesterday as unlikely to reach immediate agreement on a new general manager. If the board delays its decision, some officials said, it may soon be compelled to name an acting general manager while continuing its search.

Board members met privately yesterday afternoon to discuss possible successors to Page, but announced no decision. There were indications, moreover, that some board members may now seek to broaden the search by considering other candidates in addition to the five current contenders.

Asked for comment, Metro assistant general manager Weigle, a former Urban Mass Transportation Administration official, confirmed that he had applied for the general manager's post and said he would compete for it vigorously. "If nominated, I'd run. If elected, I'd serve," he said.

The four other reported contenders either declined to comment or could not be reached yesterday.

Page, who has headed the transit authority since 1979, will take over in June as president of the Seattle-based Washington Roundtable, a group formed recently by Washington State businesses to study economic and social problems.

The new general manager's salary is expected to be about the same as that paid to Page, who earns $77,938 annually.

Both Tucker and Wholey served previously as chairmen of Metro's board of directors. Wholey, a former Department of Health, Education and Welfare official, earned a reputation as a fiscal conservative during three terms as Arlington County Board Chairman in the 1970s.

Tucker, the D.C. City Council's first elected chairman, was narrowly defeated in a bid for D.C. mayor in 1978 and lost again in last year's elections when he sought to regain the council chairmanship. He was recently nominated by Mayor Marion Barry but rejected by a council committee as head of the city elections board.

Boleyn, a former Office of Management and Budget official, has held senior posts at Metro since 1974. Weigle came to Metro in December 1980. Tyler has been an Amtrak vice president since 1978.