Trump plans to unveil his pick to succeed retiring Justice Anthony Kennedy in a 9:00 pm (0100 GMT) televised appearance at the White House.
"We are close to making a decision," Trump told reporters late Sunday.
The choice was down to four people, he said, adding that "you can't go wrong" with any of them.
"I'll be deciding tonight or tomorrow sometime by 12 o'clock," he said.
In a later tweet he said he was looking forward to the Monday night announcement of his "exceptional" pick.
Kennedy was long a swing vote on the nine-member court, and Trump's choice -- his second opportunity in 18 months to fill a Supreme Court vacancy -- will dramatically affect many aspects of American life, from abortion to voting rights to immigration.
Conservative on firearms and election financing, Kennedy could be more progressive on issues such as abortion and affirmative action. An example of this came in 2015, when, thanks to him, same-sex marriage was legalized across the United States.
As a result, Democrats -- unable to block the nominee unless they lure some Republican senators to their side -- have stressed the high stakes of the president's decision as they prepare for the confirmation battle ahead.
Senator Dianne Feinstein said Trump's choice "could have a bigger effect on Americans' daily lives than any justice in our lifetime."
Another Democrat, Senator Richard Blumenthal, on Sunday assailed Trump's reliance on a list of potential nominees endorsed by the conservative Federalist Society.
"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," he said on ABC's "This Week."
- 'Pro-life justices' -
Democrats have sounded the alarm that Trump could shift the ideological balance of the court and thereby place women's reproductive rights, health care and LGBT rights at risk.
Trump indeed said during the 2016 campaign that he would put "pro-life justices on the court," thrilling his grassroots base although polls show most Americans support abortion rights.
Top Senate Democrat Chuck Schumer called Trump recently to warn it would be "cataclysmic" for national unity if he nominated someone hostile to Roe v Wade, the landmark 1973 decision that protects women's rights to abortion, according to a person familiar with the discussion.
Judicial experts say Trump seems to be focusing on three contenders -- federal judges Brett Kavanaugh, Raymond Kethledge and Amy Coney Barrett.
On Sunday Leonard Leo, a Federalist Society official who has been advising Trump, added a fourth name: that of Thomas Hardiman, 53, a federal appeals court judge in Philadelphia.
A fellow judge there, Maryanne Trump Barry, one of the president's sisters, reportedly has recommended him to her brother.
None of the judges named is older than 53, meaning any of them could sit on the court for several decades, allowing Trump to make a lasting imprint on the nation's laws.
Barrett, 46, is a rising judicial star and a favorite among social conservatives. As a woman and mother, she could upend the narrative pushed by Democrats that Trump's pick would erode women's rights.
But Trump appointed Barrett to the Court of Appeals for the 7th Circuit just nine months ago, and he may well leave her to gain more experience.
Kavanaugh, 53, began his career as a clerk to Kennedy. As a judge on the US Court of Appeals in Washington he has written opinions on some of the nation's most sensitive issues.
He recently voiced disagreement with a court decision allowing an undocumented teenage immigrant to get an abortion.
Kethledge, 51, sits on the Sixth Circuit appeals court. He is seen as supporting originalism, an interpretation of the Constitution along the lines of its meaning at the time of enactment.
With the Senate's Republican leadership saying it aims to complete the confirmation process before November's midterm elections, Democrats were nearing panic mode.
