James B. Burnham, special assistant to the chairman of the Council of Economic Advisers, is under consideration by the Reagan administration for appointment as the U.S. executive director for the World Bank.

The post has been vacant since the Reagan administration took office. Wilson E. Schmidt had been provisionally selected by the administration, but died last July before the appointment became official.

Schmidt is said to have played a major role in shaping the recently issued Treasury critique of multilateral bank operations.

Burnham, an economist who worked for Mellon Bank in Pittsburgh, and prior to that had been on the staff of the Federal Reserve Board, neither would confirm nor deny the report. But Treasury Assistant Secretary Marc Leland confirmed that Burnham "is under consideration."

A World Bank source said that Burnham was the Treasury's choice, but that his appointment to the $57,500 job is still "to be cleared" by the White House.

Treasury officials say that their search for a competent representative at the bank who shares Reagan administration views has been made difficult by the salary limitation. Most private-sector bankers sounded out by the administration make at least double the federal salary limit and have balked at the invitation.