All cautioned that Trump could go a different way before he reveals his choice in a prime-time address Monday.

He has said positive things to associates about Judge Amy Coney Barrett, a staunch social conservative, the people familiar with the process said, and he has not ruled out Judge Brett M. Kavanaugh, a former staff secretary to George W. Bush.

But they said he found Hardiman’s personal story to be compelling. Hardiman was the first member of his family to graduate from college, and he helped pay for his education by driving a taxi.

Hardiman has also had an important supporter within the Trump family. He served with Judge Maryanne Trump Barry, Trump’s sister, on the 3rd U.S. Circuit Court of Appeals, in Philadelphia. Barry recommended Hardiman to her brother last year as a good choice for the court, according to two people close to Trump.

Hardiman has a conservative judicial record and less baggage than some of the other contenders. He has voted to expand gun rights and to restrict court challenges from immigrants. But he has not taken public positions on other legal controversies, including abortion and affirmative action.

Trump is said to have pared his options down to four prospective justices, and Hardiman was a late addition to the grouping last week. His status as the runner-up to Justice Neil Gorsuch last year had made his chances seem dim this time around.

The only judge among the four whom the president appears to have all butruled out is Raymond M. Kethledge. People close to the process said the president had found him likable but comparatively dull.

Sen. Mitch McConnell, the top Senate Republican, has cautioned Trump that Hardiman and Kethledge would be the safest picks in terms of Senate confirmation, a process that may have to take place without any Democratic support.

This article originally appeared in The New York Times.

Maggie Haberman, Michael S. Schmidt and Adam Liptak © 2018 The New York Times