Gov. Charlie Baker is being drawn into the Never Trumpers’ seething push to oust their own party’s president, with prominent conservative Bill Kristol floating the centrist Republican’s name as a potential Trump rival in 2020.

“I don’t rule Baker out as a presidential possibility,” Kristol told Boston Herald Radio yesterday. “Baker and a moderate Democratic governor, that would be a heck of a ticket.”

The comment thrusts Baker into a national GOP squabble as the Massachusetts governor faces a challenge from staunch Trump supporter Scott Lively in the 2018 gubernatorial battle.

The affable Baker has consistently ranked as the most popular governor in America, but rumors of a presidential bid could ignite voter fears that Baker is already eyeing higher office. His gubernatorial campaign moved quick to tamp down that kind of talk yesterday.

“Absolutely not,” Baker campaign spokesman Jim Conroy said of a Baker 2020 presidential campaign. “He is grateful for the opportunity to serve the commonwealth and focused intently on delivering results for the people of Massachusetts.”

Baker has slammed Trump consistently throughout his first term, dismissing the president’s recent proposal to arm teachers in an effort to stop school gun killings.

Trump lost Massachusetts to Democrat Hillary Clinton in the 2016 presidential election, but his supporters cast more than 1 million votes for him in this state. Trump also handily won the state’s GOP presidential primary earlier that year, among nearly a dozen candidates.

Kristol, a virulent Trump critic, is a high-profile member of “Never Trumpers,” a group of moderate Republicans who oppose Trump as counter to the national party values. Baker, however, would be a perfect fit for the national party going forward, said Kristol.

“Personally I like Baker and that would be a very good model going forward,” Kristol said, adding he hasn’t talked to Baker about running.

The former Reagan administration staffer is speaking tomorrow in New Hampshire at the “Politics and Eggs” forum, which hosts prominent presidential candidates.

Kristol already attempted to recruit several people to challenge the president during the 2016 cycle, including National Review writer David French, former Massachusetts Gov. Mitt Romney, Sen. Ben Sasse and Secretary of Defense James Mattis.