He did however, let slip that four are under consideration, and most reports indicate the final candidates are current appellate judges Brett Kavanaugh of the DC Circuit, Amy Coney Barrett of the Seventh Circuit, Raymond Kethledge of the Sixth Circuit, and Thomas Hardiman of the Third Circuit.
Mr. Trump will reveal the nomination at 9 p.m.at the White House but told reporters on his way back to Washington from a weekend at his New Jersey golf club that he hadn't yet decided.
Ahead of his announcement, Trump tweeted about the stakes: "I have long heard that the most important decision a U.S. President can make is the selection of a Supreme Court Justice - Will be announced tonight at 9:00 P.M".
"He could throw a dart on that list" and conservatives would be happy.
Kavanaugh was appointed to D.C. Circuit appeals court in May 2006, after his nomination by President George W. Bush and his confirmation by the Senate.
A confirmation of Mr. Trump's nominee could give conservatives a reliable, long-term majority on the highest court.
In recent years the Supreme Court has made landmark decisions on fundamental and often politically charged issues ranging from same-sex marriage, abortion, gun rights, corporate money in elections, and free speech.
Cornyn, the No. 2 Republican in the Senate, says it's "extremely disappointing" that some Democrats have made clear they'll oppose the nominee even before the president announces his choice.
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"I've never seen a president of the United States in effect make himself a puppet of outside groups and choose from a group of right wing fringe ideologues that are prepared on this list", said Blumenthal on ABC's "This Week", accusing Trump of "outsourc [ing]" his choice to the Federalist Society and the Heritage Foundation.
"We are close to making a decision", Trump said.
The White House would love to have the Democrats' votes for confirmation.
Republicans control the Senate by a 51-49 majority, making any efforts by Democrats to thwart Trump's nominee an uphill battle.
In the coming year the court might have to consider Trump's powers and rights in the investigation into links between his presidential campaign and Russian Federation, and whether he sought to obstruct that probe.
Several senators in states where Trump won big in 2016, like Jon Tester in Montana, Joe Donnelly in Indiana, Heidi Heitkamp in North Dakota and Joe Manchin in West Virginia, are caught between the party's riled up liberal base and their own socially conservative voters.
There are no set dates for when the confirmation hearings will begin.
In a wider sense, his nominee will also represent a triumph for conservatism and the organized effort to promote vetted conservative judges that offered McConnell a pipeline of candidates for lower courts and now is reaching the ultimate prize - a solid Supreme Court majority.
"I don't think anyone should expect me to simply vote yes for this nominee just simply because my state may be more conservative than others", Mr. Jones said Sunday on CNN's "State of the Union". "I don't think my role is a rubber stamp for the President, but it's also not an automatic, knee-jerk no either", Jones said.