Top contenders for the role have included federal appeals judges Brett Kavanaugh, Raymond Kethledge, Amy Coney Barrett and Thomas Hardiman.
Mr. Thapar was on the shortlist of candidates after Judge Antonin Scalia died in 2016.
Trump during his campaign in 2016 said he would appoint justices who would overturn the landmark 1973 decision that said women have a constitutional right to an abortion.
Kavanaugh is said to have the inside track within the White House, including the support of White House Counsel Don McGahn, who's supervising the search. Just days after his inauguration in January 2017 he nominated the conservative justice Neil Gorsuch to the court.
"I think in regards to Kethledge and Tom Hardiman they are a little less known by conservatives and their records are a little bit lighter so it might take some time", Leo told ABC's "This Week" on Sunday. I think they're all outstanding. All but one of the 25 people on the list are members of The Federalist Society, a national organization of conservative lawyers, and there's a clear pattern to judicial nominees being fed by the group: They are young, conservative and have records of being very opposed to abortion rights.
Trump told reporters in New Jersey, where the president spent the weekend, that he expects to make a decision either Sunday night or by noon on Monday. Those are very terrific people. "And I believe this person will do a great job", Trump said, according to ABC News. "The whole list is extraordinary", he said.
"There's nobody that President Trump could nominate from a conservative event that will get many Democratic votes", he continued.