Martin S. Feldstein, a Harvard economist and president of the National Bureau of Economic Research, is the front-running choice to become chairman of the president's Council of Economic Advisers, succeeding Murray L. Weidenbaum, administration officials said yesterday.

Feldstein, a conservative economist who has advocated tax cuts and argued for slowing the growth in programs such as Social Security that benefit middle- and upper-income families, was one of President Reagan's original candidates for the chairmanship of the three-member economic council.

He now heads the list of candidates to replace Weidenbaum, the sources said, but Reagan has not yet approved the appointment.

Weidenbaum resigned two weeks ago to return to teaching at Washington University in St. Louis, saying he was tired and frustrated after a hectic year and a half in which Reagan won much of his program in Congress but the economy did not respond as expected.

Weidenbaum's departure left many administration officials convinced that a successor should come from the ranks of respected mainstream economists. These officials thought that feuding among the supply-side and monetarist economists who first came into the administration had damaged the credibility of Reagan's economic policies.

While Weidenbaum was not aligned with either of these two schools, he was sometimes criticized by White House insiders for giving weak advice to the president.

Feldstein, 42, has been president of the prestigious National Bureau of Economic Research since 1977. The organization has been known among economists for its impeccable scholarship and rigid nonpartisanship for more than six decades, and is better known to most Americans as the official arbiter of business cycles, deciding when the economy enters a recession or a recovery.

While Feldstein might not be the first choice of supply-siders for the CEA job, he is the first choice of many senior administration advisers and several Cabinet members, one official said. If Reagan approves the appointment, it could be announced as soon as this week, the official added. Feldstein could not be reached for comment.