When Mr. Trump spoke to a gathering of conservatives in Washington this week, Fox did not air the speech live. It instead showed a few clips after he was done speaking. That same day, it did broadcast live — for 17 minutes — a speech by former Vice President Mike Pence.
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.
The Murdochs’ discomfort with Mr. Trump stems from his refusal to accept his election loss, according to two people familiar with those conversations, and is generally in sync with the views of Republicans, like Mr. McConnell, who mostly supported the former president but long ago said the election was settled and condemned his efforts to overturn it.
One person familiar with the Murdochs’ thinking said they remained insistent that Fox News had made the right call when its decision desk projected that Joseph R. Biden would win Arizona just after 11 p.m. on the night of the election — a move that infuriated Mr. Trump and short-circuited his attempt to prematurely declare victory. This person said Lachlan Murdoch had privately described the decision desk’s call, which came days before other networks concluded that Mr. Trump had lost the state, as something only Fox “had the courage and science to do.”
Some of the people acknowledged that Fox’s current approach to Mr. Trump could be temporary. If Mr. Trump announces he is running for president, or if he is indicted, he will warrant more coverage, they said.
A spokesman for Mr. McConnell declined to comment. A spokesman for the Fox Corporation also declined to comment, as did a spokeswoman for Mr. Trump.