Senator Mitch McConnell, the Republican leader, told President Trump this past week that Judges Raymond M. Kethledge and Thomas M. Hardiman presented the fewest obvious obstacles to being confirmed to replace Justice Anthony M. Kennedy on the Supreme Court, according to Republican officials briefed on the conversation.

While careful not to directly make the case for any would-be justice, Mr. McConnell made clear in multiple phone calls with Mr. Trump and the White House counsel, Donald F. McGahn II, that the lengthy paper trail of another top contender, Judge Brett M. Kavanaugh, would pose difficulties for his confirmation…

Mr. McConnell is similarly wary of imperiling the votes of two moderate Republicans, Senators Lisa Murkowski of Alaska and Susan Collins of Maine. He has told Mr. Trump he could lose the two senators, who support abortion rights, if he picks another judge seen as a contender, Amy Coney Barrett, an outspoken social conservative who some observers believe may be more open to overturning Roe v. Wade.