Conservative commentator and outspoken "Never Trump" critic Bill Kristol says he is building a "war machine" within the Republican party to challenge 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's 2020 reelection campaign, according to CNBC.

Kristol told the network that he's preparing "for a primary run against Trump," adding that Ohio Gov. John Kasich (R) is on his shortlist of possible candidates.

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Kasich was unsuccessful in his 2016 bid for the Republican presidential nomination, only managing to beat Trump in his home state.

Kristol also said Sen. Ben Sasse Benjamin (Ben) Eric SasseTrump says he'll sign order aimed at protecting premature babies in appeal to religious voters Government watchdog recommends creation of White House cyber director position Chamber of Commerce endorses McSally for reelection MORE (R-Neb.) and outgoing Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) are also being considered.

“We are thinking of and doing preliminary work to prepare for a primary run against Trump,” Kristol told CNBC on Thursday. “People aren’t going to say they will run against Trump unless they have the infrastructure, but I’ve been trying to persuade people that it may not be that difficult.”

Kristol, who has called Trump "disgraceful" and "buffoonish," is the editor at large and founder of conservative magazine, The Weekly Standard. Kristol also serves as director of the nonprofit organization, Defending Democracy Together.

In a statement to CNBC, Sasse's spokesman did not deny that the senator has spoken to Kristol.

"I'm not going to comment on what other people decide to bring up in their personal conversations with the senator, but — like we've said for a long time — Ben doesn't pay any attention to the 2020 Washington rumor mill," said spokesman James Wegmann.

The Hill has reached out Kasich and Flake for comment.