Jeffrey D. Allred, Deseret News
FILE - Sen. Mike Lee, R-Utah, speaks as President Donald Trump looks on at the Capitol in Salt Lake City on Monday, Dec. 4, 2017.

SALT LAKE CITY — Some conservatives are pushing for President Donald Trump to fill the pending U.S. Supreme Court vacancy with Sen. Mike Lee, one of seven people the president has reportedly interviewed for the job.

But the Utah Republican isn't among the president's top choices, according to news reports Thursday.

"I think I have it down to four people. And I think of the four people I have it down to three or two," Trump told reporters aboard Air Force One on Thursday.

Trump did not name names but added that "they're all outstanding." He said he would announce his pick to replace retiring Justice Anthony Kennedy on Monday.

Sen. Ted Cruz, R-Texas, one of the Lee's closest colleagues, said Trump has a "sure thing" in Lee.

"No other candidate has his combination of record, ability and a sure-fire path to confirmation — and no other candidate would excite conservative voters this November more than someone they know and trust, like Mike Lee," Cruz wrote for Fox News.

Various news outlets have reported that Trump has interviewed seven potential nominees — Lee and federal appellate judges Brett Kavanaugh, Amy Coney Barrett, Raymond Kethledge, Amul Thapar, Joan Larsen and Thomas Hardiman.

Some reports, including the Associated Press, say the president has narrowed the field to Kavanaugh, Barrett and Kethledge. AP identified its source for that information as "a person familiar with Trump's thinking who was not authorized to speak publicly."

Republicans need a win right now and Lee is "smart politics," said David Bozell, president of ForAmerica, the largest conservative organization on social media.

Lee is a known conservative commodity who has all the credentials. Bozell said it's hard to imagine a scenario where GOP senators would vote against one of their own. If they do, he said, they would expose themselves as being the reason for the president and Congress having a sub-par legislative record.

"And even if some of these Republicans did oppose Lee — even just one — I think that boil needs to be lanced," he said.

Republicans own a razor-thin 51-49 majority in the Senate, but with Sen. John McCain, R-Ariz., unlikely to vote due to illness, that margin becomes even thinner. And Sens. Susan Collins, R-Maine, and Lisa Murkowski, R-Alaska, have set themselves up as key swing votes.

Robert Costa, a Washington Post political reporter and NBC News political analyst, tweeted Thursday: "When I asked a prominent Trump ally about Sen. Lee/ SCOTUS, they said this article is floating around the WH, as evidence that he's a long shot."

Costa included a link to an Associated Press story about Lee casting a "protest" vote in the 2016 presidential election for independent candidate Evan McMullin.

Lee, who steadfastly refused to endorse Trump, revealed his vote for president on election night.

"I've signaled in the past concerns I had with my party's nominee. I had an opportunity to register a protest vote. That's what this was," Lee told the Deseret News at the time.

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In his op-ed, Cruz said most presidents are forced to gamble on a Supreme Court nominee that they do not truly know, someone who has spent a lifetime outside the public eye and who might bend to pressure in Washington once on the high court.

But Trump, he said, has "lucked out" with Lee.

"Lee safeguards Trump’s Supreme Court legacy for all time, because there is not a single soul out there who can doubt that he would remain true to the convictions he has fought for his entire life," Cruz said.

"President Trump and conservatives can be sure that Lee won’t change."