WASHINGTON (AP) _ President Reagan told a group of state legislators he believes the Constitution should be changed to permit presidents to serve more than two terms, White House spokesman Larry Speakes said Saturday.

Speakes said the question was raised by a long-time Reagan supporter at a private meeting with legislators on Thursday in Tampa, Fla., where the president had just given a speech.

He said Reagan responded ''in a light-hearted manner'' but went on to say in a more serious vein that, while such an amendment would not apply to him, he believed that ''the people ought to have a right to decide who their leadership would be.''

Speakes said the question was couched to Reagan in terms of whether he felt handicapped by being considered a ''lame duck'' in his second term ''and he was indicating that he was going to be an active president.''

The 22nd Amendment to the Constitution, ratified in 1951, limits presidents to two elected terms and provides that no person who has filled more than two years of an unexpired term shall be elected more than once.

Until then, presidents were free to run for as many terms as they chose. Until Franklin D. Roosevelt, who died a few months after taking office for his fourth term, however, all had followed a two-term tradition established by George Washington.

President Harry S. Truman, who assumed office on Roosevelt's death and was president when the 22nd Amendment was adopted, was exempted from it. He chose not to run for a second elected term anyway.

Repealing the 22nd Amendment would require another amendment to the Constitution, which would have to be approved by two-thirds vote of both houses of Congress and by legislatures or conventions in three-fourths of the states.

Reagan met in Tampa with about a dozen members of the American Legislative Exchange Council, an organization of conservative legislators. Speakes said all but one of those meeting with Reagan were Republicans.