The "Never Trump" movement has a new ally: hedge fund boss Anthony Scaramucci, who was fired in 2017 after serving 11 days as communications director in President Donald Trump's White House.

Anti-Trump pundit and veteran Republican operative Bill Kristol confirmed to CNBC in a few brief text messages that he has spoken to Scaramucci since the SkyBridge Capital founder had a public falling out with Trump this summer. Asked whether he has spoken to Scaramucci about trying to find another presidential candidate to replace Trump on the top of the GOP ticket next year, Kristol said: "Yup."

But Kristol, who has been critical of Scaramucci in the past, wouldn't go much further than that when describing his interactions with the former Trump surrogate.

"Have chatted with him, but working with him would be an exaggeration," Kristol explained. He declined to give further details on their conversation, which he characterized as private.

Read more: Scaramucci criticizes Trump's trade war with China

Kristol's revelation offers a clue about to whom Scaramucci has been speaking regarding his criticism of Trump. While Scaramucci did not return a request for comment, he has said in other interviews that he's been getting waves of support from others since he took on the commander in chief. He has declined to name the people with whom he has spoken.

"The overwhelming flood of texts, phone conversations and support last night from people that are actually inside the White House, up on Capitol Hill, former elected officials, current people in position of power, current elected officials, is truly staggering," he said on CNN's New Day the day after he responded to Trump over social media.

Kristol has been one of the most vocal Republicans to take on the president. His previous plans include an attempt to use his nonprofit Defending Democracy Together to recruit a nominee who could primary Trump. Three of his preferred candidates – Sen. Ben Sasse, former Sen. Jeff Flake and Maryland Gov. Larry Hogan – have all said they're not going to run against Trump.

Former Ohio Gov. John Kasich, who lost to Trump in the 2016 GOP primary, has said he doesn't currently see a path of defeating a president that has a stranglehold on his party. A recent Gallup poll shows that 88% of Republican voters approve of the president.

Scaramucci, on the other hand, has been suggesting in media interviews that the GOP should push out Trump.

"A couple more weeks like this and 'country over party' is going to require the Republicans to replace the top of the ticket in 2020." he told Axios.

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Trump and Scaramucci seemed to have a cordial relationship up until this week, when their new feud took to Twitter.

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Scaramucci insists that he has no plans to back a Democrat running for the White House.