Starting from a list of 25 names vetted by conservative groups, Trump has also given serious consideration to federal appeals court judges Amul Thapar and Joan Larsen, and it's possible the White House will prepare materials for more people.
Mr Trump has chosen 9pm on Monday evening, a primetime TV slot, to make his announcement. "I think that would make it hard for West Virginia's senators to vote for a candidate like that".
Kethledge's 10 years as a federal appeals court judge give him a long record of conservative opinions that may make Trump and Republican senators feel secure about the kind of Supreme Court justice he'd be.
Lee, a member of the Judiciary Committee who was elected to the Senate in 2010, served as a clerk to Supreme Court Justice Judge Samuel Alito.
Trump's nominee must be confirmed by the Senate, where Republicans hold a narrow 51- to 49-seat majority.
Meanwhile, supporters of the various contenders lobbied heavily on Thursday, as they have all week, making phone calls to White House officials and penning newspaper opinion pieces.
Getting a successor to Justice Anthony Kennedy, who announced his resignation last week, approved by the Senate before the current session ends this year is a crucial task for Trump.
Last week, Senator Ted Cruz, another Republican conservative, said he had urged Trump to consider nominating Lee, telling the "Michael Berry Show", a radio program, that Lee "would be a justice you could trust to always be faithful to the Constitution and the Bill of Rights". The person also says it didn't seem Trump was seriously soliciting Schumer's advice since the president was already winnowing potential nominees.
President Donald Trump has spoken with Republican Sen.
Kavanaugh, 53, is a judge on the U.S. Court of Appeals for the District of Columbia Circuit who has a background in politics. Some also raised concern about his approach to the Affordable Care Act.
They say whomever President Donald Trump selects must explicitly say they support the rights to abortion, to use contraceptives and to marry someone of the same gender.
"Trump's list is full of great nominees, but Kavanaugh raises several concerns among libertarian and pro-life activists at a time when we need to be united", said Wesley Denton, communications director for the Conservative Partnership Institute, an organization that works closely with lawmakers on Capitol Hill. "Mike Lee." Lee is the only lawmaker on Trump's list of potential justices. A graduate of University of Michigan Law School, he clerked for Kennedy in the late 1990s and advised Republican Senator Spencer Abraham of Michigan. Conservative groups rallied around Barrett after her confirmation hearing past year featured questioning from Democrats over how her Roman Catholic faith would affect her decisions.
A key GOP senator is warning President Donald Trump not to repeat "mistakes" of past Republican presidents by picking a Supreme Court nominee who turns out to be insufficiently conservative. Susan Collins, R-Maine, to reject a nominee who would overturn Roe v. Wade.
Since the start of his 2016 campaign, Trump has embraced anti-abortion groups and vowed to appoint federal judges who will favor efforts to roll back abortion rights.
Kennedy said he was bracing for a tough confirmation battle as Democrats focus on the nominee's views of the high court's Roe v. Wade ruling legalizing abortion.
Outside adviser Leonard Leo, now on leave from the Federalist Society, said on ABC's "This Week" on Sunday that this kind of jockeying is standard, noting that "every potential nominee before announcement gets concerns expressed about them by people who might ultimately support them".