The president is said to have narrowed his choice to four federal appeals court judges: Thomas Hardiman, 53, of the Third Circuit Court of Appeals; Seventh Circuit Court of Appeals Judge Amy Coney Barrett, 46; Sixth Circuit Court of Appeals Judge Raymond Kethledge, 51; and District of Columbia Circuit Court of Appeals Judge Brett Kavanaugh, 53.
Kyl has a wealth of experience in the Senate, which will be needed as the president's nominee is expected to face an intense confirmation battle.
All are young enough that they could serve on the nine-member high court for decades.
Trump is set to announce his pick at 9 p.m. on Monday during a live television broadcast from the White House.
A person familiar with the selection process earlier indicated Trump was narrowing the field, with Barrett the least likely among the four to be chosen.
Trump's approach to naming a new Supreme Court justice has unnerved some Democrats.
"For the last 12 years, he has served as a judge on the D.C. Circuit Court of Appeals with great distinction, authoring 300 opinions, which have been widely admired for their skill, insight and rigorous adherence to the law", Trump said as Kavanaugh stood nearby with his wife and their two daughters in the East Room of the White House.
"Bob Casey's opposition to President Trump's nominee before he or she has even been named shows he has given up any pretense of being a moderate voice", said NRSC Spokesman Bob Salera in an emailed release. "Whoever is nominated, whoever he or she is, they're going to be there for a long time".
Kethledge serves as a judge on the U.S. Court of Appeals for the 6th Circuit in Cincinnati, Ohio.
A graduate of both Yale college and Yale Law School, he also worked under Kenneth Starr during his independent investigation of then-President Bill Clinton. Other Democrats who represent heavily Republican states will also be under pressure to support the nominee.
Barrett, who is 46, has less of a judicial record to review, having just been nominated to the appeals court by Trump a year ago. Barrett has excited social conservatives since she was questioned about her Roman Catholic faith in her nomination hearings a year ago, but her brief time on the bench has raised questions.
The appointment will not change the ideological breakdown of a court that already has a 5-4 conservative majority, but nevertheless could move the court to the right. Kennedy sometimes joined the liberal justices on key rulings on divisive social issues like abortion and gay rights, a practice his replacement may not duplicate.
Kennedy is expected to step down at the end of July.
Trump's selection will set up a confirmation showdown in the U.S. Senate, where his fellow Republicans hold a slim 51-49 majority, though with ailing Senator John McCain battling cancer in his home state of Arizona they now can muster only 50 votes.
Democrats have turned their attention to pressuring two Republicans, Sens. A more conservative majority could be more willing to uphold state restrictions on abortion, if not overturn the 45-year-old landmark Roe v. Wade decision that established a woman's constitutional right.
Trump has previously said he wanted "pro-life" justices opposed to abortion rights.
In a 2013 law review article, Kavanaugh wrote that after seeing firsthand the many hard duties that a president encounters, he thinks that presidents should operate free from the threat of civil suits, such as the sexual harassment suit that led to President Clinton's impeachment, and that presidents should also be free from criminal investigations. Not long after Schumer spoke, Senate Majority Leader Mitch McConnell accused the "far left" of engaging in "scare tactics" over the nominee. Jon Kyl, a former senior member of Senate leadership, will help guide President Donald Trump's second Supreme Court pick through the chamber's confirmation process. He has ruled against voting rights. However, he later wrote that he thought presidents shouldn't have to deal with criminal investigations or civil lawsuits while in office.