Mr. Bloomberg, he said, was a different case because of his wealth and broader, more prominent political portfolio since he left office on issues including public health, gun control and the environment.

“He has been in the forefront of issues of national interest,” Mr. Davidoff said. “And he’s in a much better position to really push that platform.”

Mr. Sheinkopf seconded this, saying that Mr. Bloomberg’s work since leaving office had only burnished his reputation, something he said would be amplified by money and all the political professionals that can buy.

“What’s different about this guy? He’s got $60 billion and a record,” he said, adding, “He’ll have the best people around him, and he’s loyal to his people.”

That said, no one who has served as New York City’s mayor has ever been elected president, a streak running back to DeWitt Clinton, who challenged James Madison in 1812 and lost after he could not win Pennsylvania.

Governors from New York have had slightly better luck, with four becoming president, though none has been elected since Franklin D. Roosevelt in 1932. Since then, others have tried and failed — Thomas E. Dewey in 1944 and 1948; Nelson A. Rockefeller in 1960, 1964 and 1968; and George E. Pataki in 2016.

Still others have contemplated bids before deciding against it: Mario M. Cuomo’s vacillations were so well known that people called him Hamlet on the Hudson. More recently, Mario’s son, the current governor, Andrew M. Cuomo, has been mentioned as a possible candidate. Like his father, he has demurred.