Fox News has imposed a “soft ban” on Donald Trump appearing on the channel, his inner circle is reportedly complaining, even as the broadcaster extends a warm invitation to other Republican hopefuls in next year’s presidential election.

The news startup Semafor reports that the cooling of relations between the former president and his once-beloved cable news channel has gone so far that a “soft ban” or “silent ban” is now holding Trump at arm’s length. The former US president has not made a weekday showing on Fox News since he chatted with his closest friend among the network’s star hosts, Sean Hannity, in September.

Meanwhile, Trump’s rivals for the 2024 Republican presidential nomination are currently frequent guests on Fox. Media Matters for America, a watchdog that keeps a close eye on the network’s output, has counted seven weekday appearances by the former governor of South Carolina Nikki Haley since she launched her presidential bid last month.

Even the lesser known right-wing activist and entrepreneur Vivek Ramaswamy, who threw his hat into the ring last week, has appeared four times on Fox. Florida’s rightwing governor, Ron DeSantis, who is widely expected to compete with Trump though he has yet to declare, is also repeatedly seen on the network.

Semafor said it based its story on information supplied by four members of Trump’s circle. It quoted an unnamed individual “close to Trump” saying: “Everyone knows that there’s this ‘soft ban’ or ‘silent ban’. It’s certainly – however you want to say, quiet ban, soft ban, whatever it is – indicative of how the Murdochs feel about Trump in this particular moment.”

The Guardian asked Fox News to confirm or deny the existence of such a ban, but did not immediately receive a reply.

The undeniable tailing off of Trump’s exposure on Fox comes at a tense moment for the network, which is battling a $1.6bn lawsuit from the voting machines company Dominion. The suit claims that Fox News Network, with the complicit approval of its parent company Fox Corp, allowed wild defamatory conspiracy theories to proliferate on its platform, falsely accusing Dominion machines of stealing the 2020 presidential election from Trump by flipping votes from him to Joe Biden.

In excerpts of a deposition given in the case by Rupert Murdoch in January, the owner and chair of Fox Corp admitted that he knew that several Fox hosts were endorsing lies about the election being stolen from Trump yet he chose not to stop them. Legal and media experts have suggested that the admission places Murdoch’s empire in considerable legal and financial peril.

During Trump’s rise to the White House in 2015-16, and his ensuing years in office, he was virtually inseparable from Fox News. He regularly made impromptu calls into his favourite shows, and in the single year 2019 posted 657 tweets responding to content aired by the channel or its sister outlet Fox Business.

In the immediate aftermath of Trump’s defeat in the November 2020 election, Fox hosts were permitted to continue broadcasting lies about massive voter fraud. But since the stolen election campaign reached its nadir on 6 January 2021, with the insurrection at the US Capitol, followed later that year by the lodging of lawsuits by Dominion and another voting machine company, Fox has gradually backed away.

In turn, Trump has increasingly vented his anger towards his former media friend. This week he posted a rant on his social media platform Truth Social in which he accused Murdoch himself of peddling “fake news” after the Fox chief was revealed to have said in a deposition that he did not believe the stolen election lie from the beginning.

“If Rupert Murdoch honestly believes that the presidential election of 2020, despite massive amounts of proof to the contrary, was not rigged & stolen, then he & his group of Maga hating globalist Rinos [Republicans in name only] should get out of the news business as soon as possible,” Trump said.

There is no evidence that the election was rigged, as numerous top officials, including Trump’s own former US attorney general Bill Barr, have attested.