Mr. Trump has spoken recently with senators and allies about trying to depose Mr. McConnell and whether any Republicans are interested in mounting a challenge, according to people familiar with the conversations. There is little appetite among Senate Republicans for such a plan, lawmakers and aides said, but the discussions risk driving a wedge deeper between the most influential figure in the Republican Party and its highest-ranking member in elected office…

Mr. McConnell declined to comment. But his grip on the party’s 50 senators appeared steadfast.

“Naw, I’m not going to get in that fight,” said Sen. Tommy Tuberville (R., Ala.), one of Mr. Trump’s top allies in the Senate. Mr. McConnell, he added, “is doing a good job.”

Republican senators vote every two years on which members to elevate as leaders, and Mr. McConnell’s eighth term in the top spot—the longest-ever tenure for a Republican leader—doesn’t end until the next session of Congress in January 2023. The record for either party is held by Mike Mansfield of Montana, who was Democratic leader of the Senate for 16 years until he resigned in 1977.