J. William Middendorf II, an active political supporter of President Reagan and president of Washington's third-largest bank holding company, is a leading candidate to head the Export-Import Bank, sources said yesterday.

Middendorf, former secretary of the Navy, was finance chairman of the Reagan inaugural committee and chairman of Reagan's transition task force on the Central Intelligence Committee and was presumed to be in the running for several top posts in the new administration.

The position that he is now a contender for, however, may have lost some of its luster recently.

The Ex-Im Bank, a federal agency that provides subsidized loans to help U.S. companies sell overseas, has been a prime target for Reagan administration budget cutters because of the impact of its fast-growing borrowing on the overall federal demand for credit.

David A Stockman, director of the Office of Management and Budget, and Deputy Treasury Secretary R. T. McNamar won a Cabinet debate against Commerce Secretary Malcolm Baldrige and U.S. Trade Representative William Brock last week, over the size of the Ex-Im Bank's budget.

Stockman and McNamar reportedly argued that the Ex-Im Bank's leading clients include Boeing Corp., General Electric Corp., Westinghouse and other powerful firms whose need for export subsidies from the Ex-Im Bank should be a low priority on the administration's list. Stockman and McNamar reportedly have won the first round, although some of the bank's clients have not abandoned the fight, sources said.

Middendorf, president of Financial General Bankshares Inc., has not been asked to take the Ex-Im Bank position, sources said, but is believed to be the front-runner.

He organized a group of local investors who recently invested $400,000 to try to rescue the bankrupt Auto-Train Corp.