Hannity’s coziness with the president, as well as that of other Fox News hosts with Trump, has at times discomfited the executives trying to steer the network in the post-Roger Ailes era. The channel is now led by CEO Suzanne Scott, and Fox News executives have at times pushed its hosts to distance themselves from the president, according to people familiar with their deliberations. On at least one occasion, executives asked a group of Fox personalities who had been invited to dine at the White House to decline the invitation, hoping to fend off the appearance that the network has inched too close to the White House.

“All it is is fear and nervousness about the whole situation,” a former network producer said of the proximity of so many of the network’s stars to the White House, including a romantic relationship between Fox host Kimberly Guilfoyle and the president’s son Donald Trump Jr. A spokeswoman for Fox News declined to comment on the record for this article.

A person close to Hannity said executives have not asked him to decline the president’s invitations and that he has “a strong working relationship with Rupert [Murdoch], Lachlan [Murdoch] and Suzanne Scott. Rupert in particular loves news and a strong, dynamic editorial division.” Unnamed sources, the sources continued, “obviously work in the much lower-rated news division at Fox, and are just jealous of the attention and ratings of the opinion hosts on the network.”