Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) urged Mississippi Gov. Phil Bryant (R) to consider appointing himself to Sen. Thad Cochran William (Thad) Thad CochranEspy wins Mississippi Senate Democratic primary Bottom Line Mike Espy announces Mississippi Senate bid MORE’s (R-Miss.) seat if Cochran decides to resign, according to The Washington Post.

McConnell reportedly spoke directly to Bryant about potential Senate plans, while the Clarion-Ledger in Jackson confirmed that President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE also discussed those plans with the governor.

Cochran, 80, has recently had health issues that raised concerns about a possible resignation, including a urinary tract infection late last year that kept him away from the Senate for several weeks.

But sources told the Clarion-Ledger that Bryant isn’t interested in a Senate seat.

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And in an emailed statement to the Post, Bryant touted Cochran’s service in the Senate and called the rumors about the senator resigning “insensitive.”

“Mississippi is stronger because of Sen. Cochran’s service, and I look forward to it continuing,” Bryant said in the statement. “Speculation about anything else is insensitive, irresponsible and unfair.”

Bryant attended Trump’s State of the Union address on Tuesday night as McConnell’s guest and the two ate together before the speech, according to the Post.

McConnell wants to protect Republicans’ slim 51-seat majority ahead of this year's midterm elections. By appointing himself, Bryant would present a roadblock for state Sen. Chris McDaniel (R), who has reportedly expressed interest in the seat if Cochran resigns.

McDaniel, a Tea Party favorite, drew the ire of McConnell and GOP leadership when he challenged Cochran in a vicious 2014 GOP primary. McDaniel is currently mulling a bid against Sen. Roger Wicker Roger Frederick WickerHillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' Republican Senators raise concerns over Oracle-TikTok deal MORE (R-Miss.).

The state senator told the Post on Thursday that he’s delaying his decision about challenging Wicker “because of the multiple options.” McDaniel said he’s heard talk of McConnell urging the governor to appoint himself in the event of a vacancy.

“McConnell’s doing his best to find someone he thinks can hold off a strong challenger,” McDaniel said in an interview to the Post. “But, I just think the people want to have their say.”