Washington (CNN) President Donald Trump spoke with Utah's GOP Sen. Mike Lee by phone on Monday about the Supreme Court vacancy, a spokesman for Lee confirms to CNN.

White House spokesman Raj Shah confirmed the call as well.

The conversation came a week ahead of Trump's self-imposed deadline of July 9 to announce his nominee to replace Justice Anthony Kennedy.

Lee is a member of the Senate Judiciary Committee, which will hold a key vote on whoever Trump nominates, and he is one of the most conservative members of the Senate.

A favorite among many on the right, Lee has never been a judge and was a prominent Trump critic ahead of the 2016 election. However, Lee's name is on Trump's list of potential choices f or the Supreme Court, and since Kennedy announced his intention to retire, Lee has kept open the possibility the President could tap him to join the court.

"I would not say no," Lee said last week after Kennedy's announcement.

Lee's brother Thomas, who is on the Utah Supreme Court, is also on the list of potential picks the White House released last fall.