Former The Weekly Standard editor Bill Kristol confirmed that he has spoken with former White House communications director Anthony Scaramucci about finding a Republican candidate to succeed Trump as the GOP's 2020 nominee.

In an exchange of text messages with CNBC, Kristol said he has been in contact with Scaramucci since his public Twitter altercation with the president a few weeks ago.

Kristol has been a fierce critic of Scaramucci in the past and would not divulge his full interactions with the hedge fund boss, calling them "private." He did, however, confirm that the pair have discussed the matter.

"Have chatted with him, but working with him would be an exaggeration," Kristol said.

Scaramucci has claimed that several people have privately sent words of encouragement to him since his Twitter feud with Trump but declined to name which specific officials have reached out.

"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," Scaramucci said on CNN's New Day after the falling-out.

Kristol has been one of the most outspoken Republican critics of Trump during his presidency. He previously sought to use his nonprofit organization Defending Democracy Together to find a Republican challenger to run in the 2020 primary against Trump.

But Scaramucci has called for an even more radical approach and suggested in a Vanity Fair interview that Trump himself would drop out of the 2020 race by March if his poll numbers continue to show him losing to Democratic candidates.

"We need an Arya Stark, okay? We gotta take this guy out because this is like the Night King," Scaramucci said.