While the president has been pondering his pick, aides have been preparing for a tough confirmation fight.
That increases the focus on two Republicans - Sen.
The process is arduous, with the private meetings giving way to days of testimony before the Senate Judiciary Committee, which has 11 Republicans and 10 Democrats. He now works for the Washington-based lobbying firm Covington & Burling.
The White House hopes Kyl's close ties to Senate Republicans will help smooth the path for Mr. Trump's eventual selection to win confirmation.
Trump is set to announce his pick at 9 p.m. on Monday during a live television broadcast from the White House.
Republicans and Democrats are gearing up for a combative confirmation process, as Republicans hold a slim majority in the Senate and liberals express fear that Trump's pick could join the conservatives on the court to someday overturn the Roe v. Wade decision.
In recent days, Trump has shown a newfound interest in Judge Thomas Hardiman, who was the runner-up previous year when he nominated Neil Gorsuch to the Supreme Court. He was said to be the leading contender in the days after Justice Anthony M. Kennedy announced his retirement. But the situation appeared to remain fluid.
Thomas Hardiman, 53, who sits on the 3rd US Circuit Court of Appeals, is also thought to be on Trump's list. But his supporters cite his experience and wide range of legal opinions.
Kethledge, a graduate of the University of Michigan Law School, is a former Kennedy clerk and a former in-house lawyer at Ford Motor Co.
But that element of his record is among the reasons that some Republicans in Congress are concerned about a confirmation hearing in the Senate.
Barrett of IN, 46, serves on the U.S. Court of Appeals for the 7th Circuit. He co-authored a book with Army veteran Mike Erwin of The Positivity Project published a year ago called "Lead Yourself First: Inspiring Leadership Through Solitude".
The Times says Trump has recently been asking associates about Hardiman, and has also been talking about Barrett and Kavanaugh. On Saturday, he tweeted that a "Big decision" was coming soon.
"Let's say it's the four people".
Sen. Lindsey Graham (R-S.C.) spoke out about this concern on the air with Fox News on Sunday.
"They're good judges", Blunt said on NBC's "Meet the Press". Add Supreme Court as an interest to stay up to date on the latest Supreme Court news, video, and analysis from ABC News.