In a recent interview with The New Yorker, the U.F.C.’s president, Dana White, said Mr. Trump brought up the idea of hosting a fight on the White House lawn. He said the two men were watching an event when Mr. Trump leaned over to him and said, “We should do a fight at the White House.”

The president may not yet be done with his devastating overhaul of one of the world’s most instantly recognizable monuments.