Both the White House and Sen. Mike Lee, R-Utah, have confirmed the Republican lawmaker was one of four candidates interviewed by President Trump on Monday to fill the empty seat on the U.S. Supreme Court vacated by retired Justice Anthony Kennedy.

Shortly after Kennedy announced last Wednesday that he was retiring from the Supreme Court, Trump said he would be choosing the Reagan appointee’s replacement from a list of 25 candidates the White House released last November. Trump said he would announce his decision on his nominee next Monday.

Sen. Mike Lee, R-Utah, and his brother, Utah Supreme Court Justice Thomas Lee, both have made Trump’s list to replace Kennedy in Washington.

As senator, Lee could ostensibly vote for himself during the confirmation hearing if Trump nominates him – something he has not ruled out.

“My understanding is that that is what the Senate rules allow and you’re still a senator until you’re no longer a senator,” Lee told Fox News last week. “You’re still a senator at the moment you’re being considered for something like that.”

The Senate Judiciary Committee has an 11-10 breakdown between Republicans and Democrats. Thus, if all Democrats stuck together, Lee would have to vote for himself for his potential nomination to be referred “favorably” to the floor by the committee.

Since World War II, only one senator - Harold Hitz Burton, an Ohio Republican – has been nominated for the Supreme Court. Burton was not confirmed.

Both Lee and his brother have spent much of their lives around the Supreme Court.

Thomas Lee, who has served as a justice on Utah’s Supreme Court since 2010, is a former law clerk to Supreme Court Justice Clarence Thomas. Mike Lee, known for his staunch conservativism, told “Fox and Friends” that he has been watching Supreme Court arguments since he was 10 “for fun.”

“I started at that age watching Supreme Court arguments just for fun, going with dad to the court," he said, "and so I’m honored just to be considered.”

The Lee brothers are the sons of President Ronald Reagan's solicitor general, Rex Lee, who argued 59 cases before the Supreme Court. The brothers also spent much of their childhood in Washington D.C.

Last week, Sen Ted Cruz, R-Texas, told Fox News’ Dana Perino that his counterpart from Utah would be the “best choice” to fill the Supreme Court vancancy.

"I think the single best choice President Trump could make to fill this vacancy is Sen. Mike Lee," Cruz said on Fox News shortly after Kennedy's announcement. "I think he would be extraordinary."

The president said last Wednesday that he would start the effort to replace Kennedy "immediately" and would pick from the list of 25 names that he updated last year. Senate Majority Leader Mitch McConnell declared that the Senate "will vote to confirm Justice Kennedy's successor this fall."

With Kennedy's departure, Republicans have a longed-for opportunity to tip the balance of the court. It already has four justices picked by Democratic presidents and four picked by Republicans, so Trump's pick could shift the ideological balance toward conservatives for years to come.

Chad Pergram and The Associated Press contributed to this report.