Hardiman, who lives in Pennsylvania, is a judge on the U.S. Court of Appeals for the 3rd Circuit, where he served at one time with Trump's sister, Judge Maryanne Trump Barry.
Another contender Judge Raymond Kethlidge made headlines blasting the IRS over its treatment of tea party groups.
In his conversations over the weekend, Trump expressed renewed interest in Hardiman _ the runner-up when Trump nominated Gorsuch, said two people with knowledge of his thinking who were not authorized to speak publicly.
Trump's pick will cement a 5-4 majority on the court for conservatives who could quite possibly dominate for a generation and, combined with his aggressive efforts to appoint judges to other federal courts across the country, ensure that the imprint of his contentious presidency will endure long after he has left office.
Trump is scheduled to announce a nominee at 9 p.m. Monday.
Barrett - a longtime Notre Dame Law School professor who became a federal appeals judge last fall - excited social conservatives with her testimony when she was questioned about her Roman Catholic faith in her nomination hearings past year.
Trump has enjoyed teasing details of his process in recent days, saying Thursday that he was down to four people and "of the four people, I have it down to three or two".
Barrett, who is 46, has less of a judicial record to review, having just been nominated to the appeals court by Trump previous year.
They are calling on Senate Majority Leader Mitch McConnell, R-Ky., to wait until after the November election to schedule a hearing and vote. He is also former law clerk to Kennedy, as is Kethledge.
News reported on Sunday night that Kavanaugh and Hardiman are getting the most attention in the decision-making process.
Meanwhile, the conservative Judicial Crisis Network said it will launch a $1.4 million ad buy in four states - Alabama, Indiana, North Dakota, and West Virginia - introducing the nominee in a favorable light. Kavanaugh worked in the administration of each President Bush and also for independent counsel Kenneth Starr in the investigation that eventually led to the impeachment of President Bill Clinton. Kethledge, 51, is a judge for the Sixth Circuit Court of Appeals. Trump is expected to pressure recalcitrant Senate Democrats into supporting his nominee by holding rallies in their states. Barrett has already crossed swords with Democrats in her Senate confirmation hearing for her current job, when California Sen.
Responding on "Outnumbered", Lisa Boothe said Blumenthal represents a blue state and will be fiercely opposed to whomever Trump chooses. Asked by reporters how many people were being considered, the president said: "Let's say it's the four people ... they're excellent, every one". I'm open to voting no. We don't know who the nominee is going to be yet", Jones told CNN's Dana Bash on "State of the Union. "I'm very confident with this president's enthusiasm and with Leader McConnell's enthusiasm that they can get anybody confirmed".