WASHINGTON—Utah Sen. Mike Lee, who has indicated his openness to being nominated to the Supreme Court, was interviewed by President Donald Trump by telephone about the post, his office said Tuesday.

Mr. Lee, 47 years old, is a libertarian Republican and an attorney who ousted a sitting Republican senator to win election to the Senate in 2010.

The interview, held Monday, was first reported by the Deseret News. Lee spokesman Conn Carroll confirmed the telephone conversation and said that it had been an interview about Mr. Lee’s potential nomination to the high court.

Mr. Trump also spoke with three potential Supreme Court nominees on Tuesday, said White House spokesman Raj Shah.

In comments last week at a town hall, Mr. Lee said that if he were asked to consider the job, “I would not say no.” Mr. Lee is on President Trump’s public list of potential nominees, and fellow Republican senators have backed him for the post.