Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) said on Wednesday that it’s up to President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE to pick a potential successor for Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE, but the nominee won’t come from the Senate.

"It's not going to come from our caucus, I can tell you that. 51-49, you can do the math. We're not doing that,” McConnell said Wednesday during an Associated Press Newsmakers interview.

Senate Republicans have previously warned Trump against firing Sessions, who served in the caucus for decades and is still widely respected by his colleagues.

But some senators have signaled they believe Trump will fire Sessions after the November midterm elections. Sessions was Trump’s first Senate supporter, but their relationship quickly soured after Sessions recused himself from the investigation into Russia's election interference.

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"Who the attorney general is is up to the president. We confirmed Jeff, most of us worked with him for a long time. But in the end, the president decides who the attorney general is and he'll have to make that call himself,” McConnell added.

McConnell’s comments also come amid intense speculation that Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) could be trying to position himself to be Trump’s next attorney general.

But Graham’s staff and Trump both shot down that chatter this week.

Trump told reporters that Graham “wants to stay right where he is.”

"Certainly I would," Trump said when asked if he would give Graham a place in his administration. "But I think he's really happy."

Months of speculation that Trump could fire Sessions or Deputy Attorney General Rod Rosenstein Rod RosensteinDOJ kept investigators from completing probe of Trump ties to Russia: report Five takeaways from final Senate Intel Russia report FBI officials hid copies of Russia probe documents fearing Trump interference: book MORE has sparked concerns about the implications for special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE’s investigation.

Rosenstein oversees that probe because Sessions recused himself.

McConnell on Wednesday declined to speculate about if he would want a successor for either Sessions or Rosenstein to protect Mueller, but indicated he was glad the president didn’t fire the deputy attorney general.

"I don't think that would have helped the president. ... I think it would not have been in his best interest to do that,” he said.