Fox News host Bill O'Reilly is gone on an extended Easter vacation, escaping the firestorm that currently surrounds him. But in his absence, Rupert Murdoch and his sons James and Lachlan continue to debate his future.

The Murdochs' hope, two sources close to the matter said, is that O'Reilly's two-week vacation will temper the media frenzy that has surrounded O'Reilly since April 1, when The New York Times revealed that he and Fox had paid $13 million in settlements to five women who'd accused him of sexual harassment or verbal abuse.

Indeed, save for one Boston affiliate's decision to drop "Fox" from the name of its newscast, because its conservative brand had become a liability for the station in the liberal area, Fox and O'Reilly were largely absent from the headlines on Friday.

But the vacation has only bought the Murdochs more time: O'Reilly is scheduled to return to his show on April 24, and sources familiar with the Murdochs' discussions anticipate that the company will have a formal announcement on O'Reilly's status by then.

There is disagreement among the Murdoch family, according to three sources with knowledge of the matter: Rupert, the executive chairman of Fox News' parent company 21st Century Fox, supports O'Reilly and chafes at the thought of caving to public pressure -- especially if that pressure is driven by outraged liberals who presume that where there is smoke there must be fire.

James, the chief executive officer, believes the smoke is harmful enough on its own, the sources said. He is embarrassed by the controversy and feels that the sexual harassment scandals surrounding both O'Reilly and Roger Ailes, the former Fox News CEO, have damaged the company's reputation.

Lachlan, also an executive chairman, is somewhere in the middle -- respectful of his father's leadership while also understanding of how 21st Century Fox's defense of O'Reilly can make it seem mired in 20th century values.

All three of the Murdochs can not fail to recognize that O'Reilly is a major financial asset, bringing in more than $100 million in annual revenue for the company. They are also likely well aware that, despite the public backlash, O'Reilly's ratings remain as strong as ever.

There are two factors that could tip their thinking on O'Reilly: The first is the internal investigation by law firm Paul, Weiss into the accusations made by Wendy Walsh, a former guest on O'Reilly's program.

Walsh has alleged that O'Reilly cancelled her segment on the show after she rebuffed his advances. Even if Fox's investigators determine that O'Reilly's behavior toward Walsh was never inappropriate, there may be repercussions. As one 21st Century Fox source noted, investigations like these are a starting point that can open up new doors of inquiry.

The second factor is the federal investigation into whether or not 21st Century Fox misled investors by hiding payments to women who accused Ailes of sexual harassment. That, too, could open new lines of inquiry into O'Reilly's history.

Spokespeople for 21st Century Fox, Fox News and O'Reilly all declined to comment.