President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE is not on board with a potential Senate bid by former Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsRoy Moore sues Alabama over COVID-19 restrictions GOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs MORE, according to Sen. Richard Shelby Richard Craig ShelbySenate to push funding bill vote up against shutdown deadline Senate GOP eyes early exit Dems discussing government funding bill into February MORE (R-Ala.).

Shelby told The Hill on Thursday that he has discussed a potential Sessions candidacy, and the Senate race more broadly, with Trump, but that the president was "not encouraging" about the former Cabinet official and longtime senator making a bid for his old seat.

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"I did talk to [Sessions]. I talked to the president about it to … about if Sessions ran, he was not encouraging," Shelby said. "How do I say it? He was not on board, OK?"

Though Shelby said he previously discussed the Alabama Senate race with Trump recently, the president's feedback on a potential bid by Sessions, his first Senate supporter, appears to be previously unreported.

Asked if the president explained why he wasn't supportive of a potential Sessions bid, Shelby declined to discuss the details of their conversation, saying he didn't want to "get into that."

"We talked about every possibility. We talked about the seat, basically, you know how to win the seat," Shelby said.

White House spokespeople didn't immediately respond to a request for comment.

Shelby said Sessions came up as part of a broader discussion about the Alabama Senate race, and that he raised his longtime Senate colleague because "he's been in the news. He's been mentioned."

"I think he would be formidable but he would [have] multi-battles. He might be having to struggle if the president was against him … and then with his opponents," Shelby added.

Sessions and Trump had a rocky relationship after he recused himself from oversight of the FBI's probe into the 2016 election and the president's campaign. The decision became a constant sore spot for the two men, culminating in the former attorney general being ousted from the Justice Department shortly after the midterm elections.

Sessions's name has floated over the Senate race for weeks amid speculation that he might try to jump in the primary fight for his old seat. He declined to discuss the matter in May when he was at the Capitol for Shelby's birthday party.

He also declined to rule out a run shortly after that while speaking at the SALT Conference in Las Vegas, where he said that the hasn't "made a formal announcement about the Senate race, but I am interested about the issues."

“I’d love to see us bring more intellectual heft behind those positions. I think it exists, and maybe I can contribute some in that,” Sessions said.

Shelby said he had talked to Sessions weeks ago but appeared skeptical that the former attorney general would run.

"I don't think he's going to run, but he hasn't said unequivocally he's not," Shelby said. "He would be a formidable candidate if he ran, but he would ask himself why would he want to come up here."

Sessions, if he were to run, would be one of several Republicans in or eyeing the race. Among the handful of candidates already in the race are Rep. Bradley Byrne Bradley Roberts ByrneBottom line Jerry Carl wins GOP Alabama runoff to replace Rep. Bradley Byrne Jeff Sessions loses comeback bid in Alabama runoff MORE (R-Ala.), former Auburn football coach Tommy Tuberville and former state Chief Justice Roy Moore Roy Stewart MooreRoy Moore sues Alabama over COVID-19 restrictions Vulnerable Senate Democrat urges unity: 'Not about what side of the aisle we're on' Sessions hits back at Trump days ahead of Alabama Senate runoff MORE.

Moore has caused an early headache for Republicans, who view him as politically damaged after he faced several allegations of sexual misconduct with teenage girls when he was in his 30s. Moore narrowly lost the 2017 special election to now-Sen. Doug Jones (D-Ala.), who is serving out the final two years of Session's term.

Shelby characterized Moore as "damaged" and unlikely to win the party's primary.

"I think Roy Moore won't win the primary," Shelby said. "Secondly, he wouldn't be good for Alabama."