Two other candidates for the seat of the retiring Justice Anthony M. Kennedy — Judge Amy Coney Barrett and Judge Raymond Kethledge — were not the focus of Mr. Trump’s morning discussions, according to those familiar with the discussions.

[Read more on Trump’s Supreme Court nominees list.]

The drama-focused president is going to announce his choice for the Kennedy seat in a Monday night address to the country at 9 p.m. He said on Sunday that he hoped to have made a decision by noon on Monday.

The president has been lobbied in the final hours of his selection process by both supporters and opponents of the four candidates, all of whom are federal appeals court judge with conservative records.

Judge Barrett, the only woman under consideration, has the support of Sean Hannity, the Fox News host and close Trump ally, who played golf with the president in New Jersey on Sunday.

Mr. Kethledge also has supporters. But he has a comparatively thin record of judicial opinions, and some conservatives have voiced concerns that he could turn out to be similar to Justice David Souter, who was appointed to the court by President George H.W. Bush but sometimes sided with the court’s liberals. Mr. Kethledge’s rulings in an immigration case have brought criticism from conservatives like the commentator Ann Coulter. And Judge Hardiman, the first in his family to graduate from college, has the kind of personal story that appeals to many Trump supporters.