Trump himself said on the campaign trail that he would look at judges William Pryor and Diane Sykes as top contenders, and has touted his list of 20 possible choices from conservative legal circles. Sources close to the search say as things stand now, Judge Neil Gorsuch has emerged on top of the list as well as Judge Thomas Hardiman.
The President will discuss the Supreme Court vacancy Tuesday afternoon with Senate Majority Leader Mitch McConnell, Minority Leader Chuck Schumer, and the leaders of the Judiciary Committee, McConnell announced.
"I appreciate the President soliciting our advice on this important matter," McConnell said.
However, Trump may have already made his choice.
"I think in my mind I know who it is," Trump said during a luncheon at his hotel Thursday with Republicans, according to cell phone video of the event obtained by CNN. "I think you're going to be very, very excited."
In recent weeks, the search has intensified as lawyers and outside groups have joined the effort pouring through legal briefs, opinions, articles and congressional transcripts.
The decision will all come down to a calculation by top staff weighing the judge and the current court against a series of factors including his or her record, age and background.
A look at four of those on the top of the list reveal arguments that Trump will weigh both for and against.
Trump knows, for example, that if he picks Pryor, he is asking for a fight with Senate Democrats. Pryor sits on the 11th Circuit Court of Appeals and he is a dream candidate for many conservatives. He's called Roe v. Wade, the Supreme Court ruling legalizing abortion, an "abomination." He's a committed member of the Federalist Society, and in the mold of the late Justice Antonin Scalia, believes that the Constitution should be interpreted based on its original public meaning.
"I am a conservative, and I believe in the strict separation of governmental powers," Pryor wrote in 1997 when he was attorney general of Alabama. "Courts should not resolve political problems."
Pryor has faced the Senate gauntlet before.
In 2004, Democrats blocked his confirmation to the appellate court, and it was only in June 2005 that he was officially confirmed by a vote of 53-45.
But despite Pryor's record, some conservatives have questioned an opinion he joined that they perceive as expanding transgender rights.
Gorsuch, who sits on the 10th Circuit Court of Appeals, based in Colorado, has never called Roe an abomination. In fact, he's never had the occasion to write an opinion addressing Roe.
That might disappoint some who want to make sure that he wouldn't surprise them on the issue.
But he's become a favored candidate in part because of his opinions on religious liberty including one he joined siding with closely held corporations who believed that the so-called contraceptive mandate of Obamacare violated their religious beliefs.
And on more than one occasion, he's aligned himself with Scalia. In the weeks after Scalia's death last year, Gorsuch gave a talk emphasizing that "the great project of Justice Scalia's career was to remind us of the differences between judges and legislators."
Trump might conclude that Gorsuch could sidestep a major fight in Congress.
Or not. Liberals are still seething mad that Republican senators failed to hold hearings for former President Barack Obama's nominee, Merrick Garland, and could take it out on Gorsuch, or anyone else Trump picks.
"Those of us who believe that Merrick Garland was improperly denied a vote and also recognize that the majority of the American people voted for Hillary Clinton are going to refuse a nominee who moves the court in such a a right wing direction," said Caroline Fredrickson of the American Constitution Society. It is unclear if progressives would accept any of Trump's nominees that have been a part of his current list.
Sykes hails from Wisconsin, a critical state during the last election and home to Trump's Chief of Staff Reince Priebus.
A former journalist, she flexed her interviewing skills in 2013 by sitting down with Justice Clarence Thomas for a talk to discuss his jurisprudence. She won over the room during the event -- hosted by the Federalist Society -- for showcasing Thomas' personality in an interview that at times brought down the house.
Just last week Sykes issued an opinion striking three provisions of Chicago regulations meant to govern shooting ranges. It was a follow up opinion from one she penned in 2011 that enjoined Chicago's ban on firing ranges within city limits. Both opinions are peppered with references to Scalia's landmark Second Amendment opinion, District of Columbia v. Heller.
Sykes would bring another woman to the Court. She would be the fifth woman ever named, the second from a Republican candidate. But Trump could calculate that it would make more sense to save her for the seat of Justice Ruth Bader Ginsburg should she ever retire.
Sykes is also 59 years old, and some court watchers think that Trump might prefer someone younger.
Hardiman of the 3rd Circuit Court of Appeals, for example, is almost a decade younger at 51 and offers Trump a compelling personal story.
Hardiman hails from a blue collar family in Massachusetts and was the first in his family to graduate from college, driving a cab to help pay his bills. Hardiman is not product of the Ivy League having attended Notre Dame and Georgetown.
Those close to him think that Trump might appreciate Hardiman's dry wit and the fact that while he is persuasive he doesn't take over a room.
Like Sykes, Hardiman referred to Heller several times in a dissent he penned in 2013 in a case concerning gun licenses.
The opposition of Hardiman has been relatively muted and Ian Millhiser of the progressive Think Progress has written that he is "one of the more ideologically enigmatic names on Trump's list." Such a sentiment could scare away conservatives who do not want a dark horse candidate.
Conservatives believe that George H.W. Bush missed an opportunity to shape the court when he named a relative unknown -- David Souter -- to the bench. Rather than helping create a conservative legacy, Souter became a reliable vote for the left. Some might question whether Hardiman has a robust enough record to scour and get Republicans excited.
If Trump needed a personal reference, however, he'd only need to reach out to his sister, Judge Maryanne Trump Barry, who sits on the same appellate bench.