In the former president’s view, according to two people who have spoken to him recently, Fox’s ignoring him is an affront far worse than running stories and commentary that he has complained are “too negative.” The network is effectively displacing him from his favorite spot: the center of the news cycle…

Mr. Trump has complained recently to aides that even Sean Hannity, his friend of 20 years, doesn’t seem to be paying him much attention anymore, one person who spoke to him recalled.

The snubs are not coincidental, according to several people close to Mr. Murdoch’s Fox Corporation who spoke on the condition of anonymity to discuss the company’s operations. This month, The New York Post and The Wall Street Journal, both owned by Mr. Murdoch, published blistering editorials about Mr. Trump’s actions concerning the Jan. 6, 2021, riot on the Capitol.

The skepticism toward the former president extends to the highest levels of the company, according to two people with knowledge of the thinking of Mr. Murdoch, the chairman, and his son Lachlan, the chief executive. It also reflects concerns that Republicans in Washington, like Senator Mitch McConnell of Kentucky, the minority leader, have expressed to the Murdochs about the potential harm Mr. Trump could cause to the party’s chances in upcoming elections, especially its odds of taking control of the Senate.