A spokesman for Kasich, one of the most vocal Republican critics of President Donald Trump, did not deny he's signing with either CNN or MSNBC. The spokesman also noted that any decision he makes about going on cable will have no impact on whether he runs for president.

These people added that Kasich could announce his plans as early as Tuesday, a person close to Kasich said.

These people would not say the role Kasich will play at a network, only to say that he's ruled out joining Fox News Channel. Kasich hosted his own show on Fox News for several years in the 2000s.

Kasich has signaled to close advisors and some donors that he is looking to sign with either CNN or MSNBC as he finishes his two-term tenure as Ohio's governor, according to three people with knowledge of the conversations, including two who have been close to the governor since his 2016 presidential run.

Republican John Kasich, who is thinking about running for president in 2020, is likely to announce as soon as this week that he will join a major cable news network, CNBC has learned.

"Any announcement about a TV contract would have no bearing on his 2020 intentions," chief political spokesman Chris Schrimpf told CNBC in an email. "All options are still on the table."

Kasich has often appeared on CNN and MSNBC, where he has criticized the president for the implementation of tariffs and his border wall proposal, among other issues.

MSNBC declined to comment, and a CNN representative did not immediately respond to a request for comment.

One of the people who spoke to CNBC on the condition of anonymity has been a top donor for Kasich since his last run for president. This person insisted that he has still not ruled out running for the White House in 2020, even as he prepares to get involved with cable news.

"Of course it doesn't mean that he's not running. All options remain on the table," this person said.

Charlie Black, a former advisor to Kasich's 2016 presidential campaign, told CNBC in an email that he believes Kasich could still run for president, but he'd have to distance himself from a career in television if he jumped into the race.

"In the past, people who run give up their network gig. It has to to do with Federal Communications Commission fairness rules. Look at Mike Huckabee and Newt Gingrich cases," Black said.

Kasich hinted in a recent interview with BuzzFeed that he hasn't finalized any plans and that an announcement could come on Monday.

"It's got to wait till Monday," he said when asked about his plans. "Nothing yet I really have finalized. There's a few things that are firm. But it's very complicated what you can do while you're in [office]. There will be a flurry of activity next week. Bread's in the oven."

The Daily Beast reported in October that Kasich has met with CNN President Jeff Zucker and MSNBC President Phil Griffin. During the meeting with Zucker, he was reportedly accompanied by Jay Sures, the president of top talent management firm, United Talent Agency.

UTA announced Monday that it had signed Kasich as a client.

"I'm excited to work with UTA to keep my voice active across the world and share my experiences and observations to help improve the lives of others," Kasich said in a UTA press release.