President Trump poured cold water on the idea of serving a third term, an idea he has frequently teased but is prohibited by the Constitution, and instead floated Vice President JD Vance or Secretary of State Marco Rubio as possible successors in an interview aired on Sunday.

Mr. Trump said in the interview, with NBC’s “Meet the Press,” that he was reluctant to be drawn into a debate about who could follow him, but he called Mr. Vance a “fantastic, brilliant guy” and Mr. Rubio “great.” Mr. Trump added that “a lot” of people are great, but said, “certainly you would say that somebody’s the V.P., if that person is outstanding, I guess that person would have an advantage.”

Mr. Trump has often mused about the idea of a third term, going so far as to say in March that he was “not joking” about the possibility and suggesting there were “methods” of circumventing the 22nd Amendment, which says no person may be elected president more than twice. Last month, his family business began selling “Trump 2028” merchandise — some with the phrase “Rewrite the Rules” — that added to the speculation.

On Sunday, the interviewer, Kristen Welker, asked Mr. Trump about that merchandise, and the president insisted that many people wanted him to seek another term before he played down the idea.

“It’s something that, to the best of my knowledge, you’re not allowed to do,” he said before adding that he did not know if the prohibition — which is part of the Constitution — was constitutional.

“There are many people selling the 2028 hat, but this is not something I’m looking to do,” he said. “I’m looking to have four great years and turn it over to somebody, ideally a great Republican.”

Four years, Mr. Trump added, was enough time to do something “really spectacular.”