Allies of John Kasich are divided about whether the term-limited Ohio governor should enter the state's upcoming Senate race now that Republican frontrunner Josh Mandel has withdrawn.

Soon after Mandel’s surprise announcement Friday — the state treasurer cited a health issue involving his wife — Kasich strategist John Weaver moved to squash the speculation.

“No,” Weaver told BuzzFeed News. “He could [run] but isn’t. And won’t.”

Weaver, who guided Kasich’s unsuccessful presidential bid in 2016, added: “There are bigger fish to fry” — a reply that underscores Kasich’s lingering national ambitions.

But several Ohio Republicans said Weaver should not be so quick to dismiss a Kasich candidacy and are encouraging the governor to reconsider running for the Senate seat. They argue Kasich would be the GOP’s strongest challenger against Democratic incumbent Sen. Sherrod Brown.

“That’s what I believe will be best for our ticket,” Matt Borges, a former Ohio Republican Party chairman and key Kasich backer, wrote in a text message to BuzzFeed News.

Borges’ wish was echoed by another operative close to Kasich’s team. Others agreed with Weaver’s response. “Time for the next chapter,” said another Kasich insider.

Kasich’s reasons for not wanting to run are not hard to understand: Brown is seen as a formidable incumbent, and national Republicans were not widely optimistic about picking up the seat in this year’s midterm elections before Mandel dropped out. Kasich has sent signals that he would like to run for president again, possibly against President Trump in a 2020 Republican primary or as an independent. Losing a Senate race in a state where he’s served two terms as a relatively popular governor would not be helpful. (And losing is a more likely scenario in Ohio than in, say, Utah, where Trump critic Mitt Romney is now seen as a likely Senate candidate.) Kasich has in the past been vehemently opposed to the idea of running for Senate, despite his differences with Mandel.

Mandel, who was seeking a rematch with Brown after to losing to him in the 2012 Senate race, was favored to win the GOP primary. But he was facing a stronger-than-anticipated challenge from Michael Gibbons, a wealthy investment banker who has won some key endorsements.

“Our prayers go out to Josh, his wife, and family,” Gibbons said in a Friday afternoon statement. “For months we have been laying the groundwork to defeat Sherrod Brown in November with one of the strongest grassroots organizations of any outsider in Ohio. Now is the time for Republicans to unite as one so we can defeat Sherrod Brown.”

Kasich considerations aside, it's far from certain that Ohio Republicans will now unite around Gibbons. Several Republican sources said they expected significant efforts to recruit US Rep. Jim Renacci or Lt. Gov. Mary Taylor into the race. Both are currently underdogs in a crowded gubernatorial primary — and sources close to both teams confirmed to BuzzFeed News that they are fielding calls to run. Gibbons, perhaps sensing the push for a more politically established candidate, pledged later Friday to pump an additional $5 million of his own money into his campaign.

Another possibility is J.D. Vance, author of the 2016 best-selling memoir Hillbilly Elegy. Key Ohio Republicans close to Kasich had encouraged Vance last year to challenge Mandel for the nomination, but Vance decided against a run in September. A source familiar with Vance’s thinking said Friday that Vance might entertain second thoughts now that Mandel has dropped out, but that such talks have not yet happened, as the news took nearly every Ohio Republican by surprise.

Potential candidates have just over a month to make up their minds: the filing deadline for Ohio’s May 8 primary is Feb. 7.