All of the candidates were on a list of 25 names released by the president in November.
Sources have told NPR that those four finalists are all US appeals court judges; Brett Kavanaugh, Amy Coney Barrett, Raymond Kethledge and Thomas Hardiman.
"Republicans are holding four lottery tickets, and all of them are winners", Graham said.
Leo said: "Brett Kavanaugh and Amy Barrett have a lot of name recognition among supporters of the president, and I think that ultimately when people like them are nominated, you'll see a lot of folks line up".
Also noteworthy: Republicans now hold more seats in state legislatures across the country, so if the last decade is any indication, new pro-life laws could be on the way.
Some conservatives have expressed concerns about Kavanaugh - a longtime judge and former clerk for Justice Kennedy - questioning his commitment to social issues like abortion and noting his time serving under President George W. Bush as evidence he is a more establishment choice.
Meanwhile, Americans for Prosperity, a group backed by mega-donors Charles and David Koch, is ready to spend over $1 million to back Trump's nominee, Politico said.
"I'm not sure I'm leaning anywhere on those four nominees". "I don't think my role is to rubber stamp for the president, but it's also not an automatic knee-jerk no, either".
Leo, who had helped Trump compile the original list of nominees, said that he would pick Kavanaugh, with Kethledge and Barrett a close second.
They are calling on Senate Majority Leader Mitch McConnell, R-Ky., to wait until after the November election to schedule a hearing and vote. All three voted to confirm Gorsuch and are up for re-election in states that Trump won handily. Previous lobbying efforts by McConnell - including a push for fellow Kentuckian 6th Circuit Court of Appeals Judge Amul Thapar, who would have been the court's first Asian-American nominee - have failed. But in terms of selecting his nominee, the president said he would not use Roe v. Wade as a litmus test for a nominee. In a recent case involving abortion and immigration, he wrote a decision that temporarily barred a pregnant teenager in immigration custody from obtaining an abortion. Susan Collins, of ME, to speak out, told Stephanopoulos last week that a candidate who would overturn Roe v. Wade "would not be acceptable", because it indicates an "activist agenda" she didn't want to see in a judge. Previously, Collins voted for Gorsuch because of his belief in the significance of precedent. Now, with a vacancy on the bench, Trump can fulfil another of his campaign promises.
Kethledge, 51, sits on the Sixth Circuit appeals court.
Hardiman has a personal connection to the president, having served with Trump's sister on the 3rd U.S. Circuit Court of Appeals in Philadelphia. Barrett, in her mid-40s, is a judge for the Seventh Circuit Court of Appeals; she was nominated by Trump.
Leo said Hardiman of Pennsylvania and Kethledge of MI are "a little bit less known by conservatives".
Barrett has a thin resume as a judge but has amassed a formidable and respected body of scholarly work. He had previously worked with independent counsel Kenneth Starr in the investigation of President Bill Clinton, and was involved in the Florida presidential vote recount in 2000. "Like Justice Gorsuch. We hit a home run there, and we're going to hit a home run here", he said.
"I'm very close to making a decision", Trump said. On Sunday he was back to citing "the four people". "You can't go wrong".