Fox News has notified Tucker Carlson that his new Twitter show, which debuted this week, is in violation of his contract with the network, Axios reports.

According to the outlet, Fox News’ general counsel sent a letter to Carlson’s lawyers notifying them of the alleged breach shortly after he released the first episode of his Twitter show on Tuesday.

In a statement provided to Axios, Carlson’s attorney said targeting his new show was akin to targeting his right to free speech: “Fox defends its very existence on freedom of speech grounds. Now they want to take Tucker Carlson’s right to speak freely away from him because he took to social media to share his thoughts on current events.”

In April, Fox News made the bombshell announcement that Carlson quietly left the network, issuing a statement that said they had “agreed to part ways,” adding, “We thank him for his service to the network as a host and prior to that as a contributor.”

The bombastic news personality has remained largely out of the spotlight since then, but on Tuesday, he debuted the first episode of his new show, Tucker on Twitter. So far, only one 10-minute episode has been posted to the social network.

According to Axios, Carlson’s contract with Fox News includes a line that reads: “Mr. Carlson’s services shall be completely exclusive to Fox.” The outlet further reports that, according to a source, Fox hopes to keep Carlson off of any airwaves, Twitter or otherwise, until 2025.

The network has not yet responded to PEOPLE’s request for comment.

Tucker Carlson.

Carlson was featured prominently in a $1.6 billion lawsuit brought against Fox News by voting equipment company Dominion Voting Systems, which was the target of election fraud conspiracies in the wake of the November 2020 presidential election.

The voting company recently settled with the network, but not before text messages and emails by Carlson and other Fox personalities were made public as part of court filings.

In one of the exchanges made public, Carlson vented about his “hatred” of former President Donald Trump, and in others he criticized the management at Fox News.

While many of Carlson’s messages were made public, hundreds of pages of documents from the Dominion lawsuit were not, raising questions about what else the now-former Fox News host may have said about his colleagues and managers.

That Carlson’s former top producer Justin Wells has also left the network (according to multiple outlets, including ABC News) adds to the theory that the exit could have stemmed from private conversations that came to light as part of the recent lawsuit.

The network ultimately settled its lawsuit with Dominion for $787.5 million dollars, though other legal issues persist.