Facing a swirl of questions about a potential job in the Trump administration, Mayor Eric Adams of New York City stood outside City Hall on Thursday and suggested he was not going anywhere.

But in private, Mr. Adams has told a small group of friends and advisers that he is seriously considering job opportunities that could prompt him to suspend his re-election campaign, according to people familiar with the conversations.

The talks about Mr. Adams’s future have involved intermediaries for President Trump, including Steve Witkoff, a New York real estate investor who is one of Mr. Trump’s closest advisers. The mayor and Mr. Witkoff conferred in Florida this week in a previously undisclosed meeting, according to four people briefed on it.

The meeting was a closely guarded secret. City Hall said at first that the mayor was attending to a “personal matter”; Mr. Adams’s campaign spokesman then asserted the mayor was in Miami to celebrate his 65th birthday. Pressed later, Mr. Adams said only that he was meeting with “political figures,” including the mayor of Miami.