It was late summer when New York City’s mayor, floundering under the cloud of scandal and ties to disreputable figures, was in need of a presidential rescue.

The year was 1950. The mayor was William O’Dwyer, the president was Harry S. Truman, and the form of rescue was a cushy ambassadorship to Mexico.

Seventy-five years later, history may be repeating itself.

Close advisers to President Trump have crafted a plan for him to nominate Mayor Eric Adams to be ambassador to Saudi Arabia, in an effort to end the mayor’s long-shot campaign for re-election in New York City, according to four people familiar with the discussions.

Steve Witkoff, a billionaire real estate investor and adviser to Mr. Trump, had actively pursued the matter, meeting personally with Mr. Adams this week in Florida and speaking with other people close to him.

Mr. Adams, a Democrat who is running a third-party candidacy, said late on Friday that he intended to stay in the race. He did not directly address the possibility of taking an ambassadorship, and took no questions.

Mr. Adams may be in need of a face-saving escape: He is running fourth in public opinion polls.

Like Mr. Adams, William O’Dwyer was a former police officer who was elected mayor. Unlike Mr. Adams, he was never accused of a crime. O’Dwyer was first elected in 1945.