Megyn Kelly talked about Donald Trump's insults. She talked about Roger Ailes's sexual harassment and Bill O'Reilly's jabs, and at the end of an interview on Wednesday's episode of “CBS This Morning,” host Gayle King had one last question for Kelly: “And you plan to leave Fox when?”

“Oh, stop!” Kelly replied, as King and co-hosts Charlie Rose and Norah O'Donnell laughed.

King's question was a joke, but also not a joke, reflecting rampant speculation that after a year of conflict, Kelly will move on from Fox News when her contract expires in July.

Kelly appeared on CBS to promote her new book, “Settle for More,” in which she likens Trump's rhetorical attacks during the Republican presidential primary to the antics of a middle-school bully and makes detailed allegations against Ailes, who resigned as Fox News chairman in July after former anchor Gretchen Carlson filed a lawsuit accusing him of unwanted advances and more than two dozen women came forward with similar stories.

Kelly writes in the book that early in her career, Ailes routinely made “inappropriate sexually charged comments” and that after several months he “crossed a new line — trying to grab me repeatedly and kiss me on the lips.” Ailes has denied harassing Kelly.

Kelly's colleagues have not been universally supportive of her decision to speak up, first in a probe ordered by 21st Century Fox after Carlson sued and now in the book. The New York Times reported shortly after Ailes's ouster that “some are resentful toward Ms. Kelly for cooperating with lawyers brought in by the network's parent company, 21st Century Fox, to investigate Mr. Ailes's behavior.”

Asked about Kelly's book during his own appearance on “CBS This Morning” on Tuesday, O'Reilly bristled and said, “I'm not interested in making my network look bad.” Then he expanded on the thought during his prime-time show:

If somebody is paying you a wage, you owe that person or company allegiance. You don't like what's happening in the workplace? Go to human resources or leave. I've done that. And then take the action you need to take afterward if you feel aggrieved. There are labor laws in this country. But don't run down the concern that supports you by trying to undermine it.

Responding to those remarks on Wednesday, Kelly said she received the blessing of Fox executives Rupert and Lachlan Murdoch to include her accusations against Ailes in the book.

“We were all on the same page that this was an important chapter to include, and I am proud of them that they feel as I do, which is sunlight is the best disinfectant,” Kelly said.

“So you don't believe you're making the company look bad, as Bill O'Reilly alleged?” O'Donnell asked.

“I believe that Roger Ailes made the company look bad,” Kelly responded.

The Murdochs' support might be enough to make Kelly want to stay at Fox News, but it appears that some colleagues hold her at least partly responsible for tarnishing the network's reputation — even though she says wasn't the alleged perpetrator in the episode she describes. That can't be a great feeling, and it has King and others thinking that Kelly's days at Fox News could be numbered.