Sessions: Don’t bet on me being Trump's VP

Donald TrumpDonald John TrumpKey takeaways from the Arizona Senate debate Major Hollywood talent firm considering rejecting Saudi investment money: report Mattis says he thought 'nothing at all' about Trump saying he may leave administration MORE’s lone Senate supporter threw cold water on the notion that he might be chosen as the Republican presidential hopeful's running mate on Thursday.

Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsFBI investigated whether McCabe leaked info about Flynn and Trump to media Ex-Senate Intel staffer pleads guilty to lying to feds over contacts with journalists House Judiciary chairman threatens to subpoena Rosenstein MORE (R-Ala.) told reporters outside the Senate chamber that he has no expectation of being Trump’s vice presidential candidate and has not spoken with him about who could be on the ticket.

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“I think that would not happen,” Sessions said. “I have not talked with him about it.”

“Don’t bet any money on me.”

Trump has claimed in recent interviews that he would likely pick an established politician as a running mate if he were to become the GOP presidential nominee.

Trump would choose “somebody that can walk into the Senate and who’s been friendly with these guys for 25 years, and people for 25 years, and can get things done,” he told The Washington Post in an interview published over the weekend. “So I would 95 percent see myself picking a political person as opposed to somebody from the outside.”

The comments raised speculation that Sessions — the only current member of the Senate to have endorsed Trump’s presidential bid — might be on the short list.

The betting website Paddy Power is offering 9-to-1 odds that Sessions will be the Republican vice presidential candidate; that’s better than the 10-to-1 odds for Sen. Marco RubioMarco Antonio RubioDating app for Trump supporters leaked its users data on launch day: report Overnight Defense: Trump says 'rogue killers' could be behind missing journalist | Sends Pompeo to meet Saudi king | Saudis may claim Khashoggi killed by accident | Ex-VA chief talks White House 'chaos' | Most F-35s cleared for flight Democrats torch Trump for floating 'rogue killers' to blame for missing journalist MORE (R-Fla.), a former presidential candidate.

Trump has faced a tremendous amount of opposition from within his own party, raising questions about whether he will be able to secure the 1,273 delegates necessary to be the nominee before the summer convention.

In recent weeks, he has been in contact with prominent Republican lawmakers including Sens. Orrin HatchOrrin Grant HatchHatch mocks Warren over DNA test with his own results showing '1/1032 T-Rex' Romney defends Trump’s policies as ‘effective,' disputes he led 'never Trump' movement GOP fractured over filling Supreme Court vacancies in 2020 MORE (Utah) and Tom CottonThomas (Tom) Bryant CottonFlake: Congress should not continue Kavanaugh investigations GOP senator suspects Schumer of being behind release of Ford letter Susan Collins becomes top 2020 target for Dems MORE (Ark.), which some have interpreted as an attempt to unify the party.

Hatch on Thursday told reporters that he talked by phone with Trump last month, and that it had been a "very decent conversation.”

“I think highly of him, there's no question about it,” Hatch said.

In coming weeks, that type of outreach appears likely to intensify. It has been reported that Trump's campaign will begin regular meetings with lawmakers on the Hill, starting as early as next week. 

“I think we’ll be able to see a strengthened Washington presence, which I support,” Sessions said. “And I think we’re going to see a slowdown in the rapidity of these primaries, a better opportunity for him to begin to talk personally with more key people. “ 

Naomi Jagoda contributed