Since political pundit Tucker Carlson’s departure from Fox News, speculation is swirling about the cable host’s next move. Some political bettors seem to think that he’ll end up on the Republican presidential ticket.

On Monday, the network fired Mr. Carlson without as much as an opportunity to say goodbye, sparking a round of speculation about why it was forcing him out and what the top cable host would do next.

As soon as the news broke, sportsbooks and betting markets started letting bettors wager on questions such as where Mr. Carlson’s next “permanent position” or “media job” will be.

A considerable number bettors are wagering that Mr. Carlson will end up on One America News, Newsmax, MSNBC, or even foreign networks like the BBC, Al Jazeera, or RT (formerly Russia Today).

So far, RT is the only network to offer him a position, doing so over Twitter earlier this week. The Russian ambassador to the United Nations, Sergey Lavrov, also took an interest in Mr. Carlson, calling his exit “curious news” at a press conference Tuesday.

So far, Mr. Carlson hasn’t hinted at what he plans to do. Speaking briefly to the Daily Mail, he said that “retirement is going great so far,” on Tuesday night.

“I haven’t eaten dinner with my wife on a weeknight in seven years,” Mr. Carlson said before driving away.

Observers with an appetite for risk are willing to bet that Mr. Carlson will leave the cable world entirely. According to political betting tracker Smarkets, Mr. Carlson jumped to fourth most likely Republican vice presidential pick from not even being on the map following the announcement.

The Smarkets tracker puts Mr. Carlson’s chances, in the opinion of bettors, at around 17 percent, putting him behind a Michigan gubernatorial candidate, Tudor Dixon, a one-time Arizona gubernatorial candidate, Kari Lake, and Ambassador Haley.

President Trump is considered the heavy favorite for the Republican nomination by betting markets — currently Smarkets gives him a 66 percent chance of winning — but some bettors appear to think that Mr. Trump might pick Mr. Carlson as his running mate.

There are others, both in the press world and in the GOP presidential field, pushing for Mr. Carlson to enter the race, even if his chances of winning the nomination are slim.

A businessman who is a Republican presidential candidate, Vivek Ramaswamy, told Politico: “I think he’d be a good addition to the race.

“I think someone should only do this if they feel called to do it, but I think it’d be good for the country if he got in, to be honest with you,” Mr. Ramaswamy said. “Tucker was one of the great political thinkers and commentators of our time.”

Other conservative influencers have claimed that Mr. Carlson is already on Mr. Trump’s shortlist of potential running mates. A conservative pundit, Nick Adams, claims that the words have already “penetrated my ears” that Mr. Trump is considering Mr. Carlson as a running mate.

“I just had an intimate conversation with a top GOP confidant who told me, on the condition of anonymity, that Tucker Carlson is ‘deep’ in talks to become President Trump’s running mate,” Mr. Adams said. “This would be a brilliant political move by President Trump and effectively end the entire 2024 race.”

This would suggest that Mr. Trump is willing to forgive Mr. Carlson for private texts that were made public in the course of a recent defamation suit against Fox News. In those texts, Mr. Carlson said of Mr. Trump, “I hate him passionately” adding, “I can’t handle much more of this.”

Mr. Carlson later walked back those statements on air on WABC radio, saying he was “enraged” that those texts were released and adding: “I love Trump.”