President Reagan believes that former Environmental Protection Agency administrator Anne M. Burford "should be compensated if it is appropriate" for her legal fees stemming from investigations of the agency in 1983, the White House said yesterday.

Burford has asked the White House to pay $211,000 in legal fees, saying that former White House counselor Edwin Meese III promised her that the administration would pick up the tab if she resigned from the EPA in 1983.

"The president's feeling on it is that Mrs. Burford should be compensated if it is appropriate and it should be at a level decided upon that is appropriate," spokesman Larry Speakes said.

Speakes said that "it will be a legal question as to whether it's proper and appropriate" and that White House counsel Fred F. Fielding referred the matter to the Justice Department and the EPA.

A Justice Department spokesman said yesterday that government funds exist to pay such legal fees, but had no other comment. Speakes said Meese, who is now attorney general, would "certainly do the proper thing if it was in his department" and disqualify himself from the decision if necessary.

Speakes said "no one that is here on the senior staff in the White House was aware of" any promise that Meese made to Burford.

"You'll have to ask Meese, and you'll have to ask Meese as to whether, what the proper thing for him to do [is] if his department is involved in it," Speakes said. The issue is for the Justice Department and the EPA to "work out," he said. CAPTION: Picture, Anne M. Burford . . . seeks $211,000 for her legal bills.