The ban was first reported in Semafor, which cited four members of Mr Trump's "inner circle" on condition of anonymity.
One of the sources said that "everyone knows" the bans exist, and that they are "indicative of how the Murdochs feel about Trump in particular moment."
Mr Trump's last Fox News appearance was in November, when he officially announced his presidential candidacy. The former president's last weekday appearance on the network was in September, during which he famously told Sean Hannity that he could declassify documents just "by thinking about it."
While Fox News hasn't hosted Mr Trump since last year, it has provided a platform to his potential rivals.
Citing Media Matters data, the Semafor report found that Nikki Haley had been featured on the network seven times since announcing her presidential bid. The barely-known Vivek Ramaswamy has made four appearances on the network, and Florida Governor Ron DeSantis has been regularly featured for weeks.
A Trump aide said the network had been increasing its efforts to "give more fair coverage, or fair airtime" to Republicans who aren't Mr Trump.
“I don’t think they’re trying to reverse course, but they’re trying to appease, and tamp down, some of that criticism.”
One of the aides who spoke to the publication said they had heard from Fox News directly that the former president was "soft banned”. Despite the alleged ban, Mr Trump is reportedly trying to secure appearances on the network in the coming weeks.
“The understanding is that they’re [Fox] not to have Trump on for an interview, because the Murdochs have made it pretty clear they want to move on from Trump … Fox is showing that by not having him on,” one of the Republican sources told the outlet.
There may be some evidence suggesting such a ban is plausible — documents made public in the Dominion Voting Systems defamation case against Fox News included instructions from Rupert Murdoch to "make Trump a non-person" in the wake of the Capitol riot.
That revelation predictably set off Mr Trump, who rushed to his Truth Social site to fire off a message calling Mr Murdoch a RINO and suggesting he leave the "News Business."
“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 should get out of the News Business as soon as possible, because they are aiding & abetting the DESTRUCTION OF AMERICA with FAKE NEWS,” Mr Trump wrote.
He continued his attack on Thursday, saying Mr Murdoch should “apologize to his viewers and readers for his ridiculous defense of the 2020 Presidential Election,” before revisiting his usual lies about the election.
“How many forms of cheating and rigging does he have to see? He should also apologize to those anchors who got it right, and fire the ones who got it wrong, or were afraid to speak up (of which there were many!). It’s time to get rid of Fake News, and call it like it is!” he wrote.
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