Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) on Monday demurred when asked if he supports renaming a Senate office building after GOP Sen. John McCain John Sidney McCainAnalysis: Biden victory, Democratic sweep would bring biggest boost to economy The Memo: Trump's strengths complicate election picture Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (Ariz.).

“We’ll be talking about the best way to honor Sen. McCain,” McConnell told reporters when asked about the idea of renaming the Russell Senate Office Building after McCain, after giving a speech memorializing McCain on the Senate floor.

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Pressed on if renaming the building was something he was would support, McConnell, who routinely doesn’t respond to hallway questions, didn’t answer as he walked into his office.

Sen. John Cornyn John CornynQuinnipiac polls show Trump leading Biden in Texas, deadlocked race in Ohio The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (R-Texas), the No. 2 Senate Republican, said on Monday that there would likely be a “discussion” and suggested the Rules Committee could take up the issue.

Senate Minority Leader Charles Schumer Chuck SchumerPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' 3 reasons why Biden is misreading the politics of court packing Cruz blocks amended resolution honoring Ginsburg over language about her dying wish MORE (D-N.Y.) is expected to offer a resolution to rename Russell after McCain. The building is currently named after former Georgia Democratic Sen. Richard Brevard Russell, who opposed numerous efforts to pass civil rights legislation.

Schumer told reporters on Monday that he had picked up some Republican support for his resolution but was unsure when he would try to move it.

GOP Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (Ariz.) said over the weekend that he would support the resolution.