It'd solve one problem for James Murdoch if Bill O'Reilly didn't come back from his current vacation.

O'Reilly is the host of what remains Fox News's most popular show, even after revelations the network and the anchor resolved sexual harassment allegations by paying his accusers a reported $13 million and dozens of advertisers pulled their spots from "The O'Reilly Factor".

The problem for Murdoch, 21st Century Fox's chief executive officer, is perception — that Fox isn't willing to jeopardise the estimated $US200 million in advertising revenue the host pulls in every year by sending a message that inappropriate behaviour toward women won't be tolerated. The network has an uncomfortable track record as it is: Roger Ailes was ousted as Fox News president last year under similarly embarrassing circumstances.

"All I can say is we want it dealt with," said Brett Harris, an analyst at Gabelli & Co, which holds millions of Fox shares. "Fox is much bigger than O'Reilly."

Women's advocacy groups including UltraViolet and the National Organisation for Women have called for O'Reilly to be fired. The uproar is a distraction at a time when Fox is trying to secure regulatory clearance for its $US14.6 billion acquisition of Sky, said Brian Wieser, an analyst at Pivotal Research who has a buy rating on Fox shares.

"Wall Street doesn't want to have to think about this," Wieser said. He said Fox News, which has routinely beat competitors for years, is strong enough to withstand a change in anchors. "You could probably put a monkey in the seat and as long as it spouted appropriately conservative views there would be decent ratings."

Wieser estimates "The O'Reilly Factor" pulls in about $US200 million a year in ad sales, based on the network's total revenue. He has been cutting back on his schedule however, with Friday's now described as "The Friday Factor" with alternating hosts.

Family decision

To help boost morale, Rupert Murdoch praised employees on Thursday morning in a memo seen by Bloomberg News, praising them for delivering Fox News's highest-rated quarter ever.

O'Reilly, 67, is taking what he called a long-planned holiday and is scheduled to return to the air on April 24. New York magazine reported that James Murdoch wants the break to become permanent. People close to the company said the anchor was due to return.

Fox has said it investigates all complaints and that it hired Paul, Weiss, Rifkind, Wharton & Garrison — the same law firm it engaged last summer after Ailes was sued for sexual harassment — to continue to look into the allegations.

The New York Times published a report earlier this month that claimed O'Reilly made sexually charged remarks and overtures to at least five female employees whose complaints the network or the TV host settled out of court. Among his defenders has been President Donald Trump, who in an interview with the Times called him "a good person" and said, "I don't think he did anything wrong".

It's not be solely up to the Fox CEO to determine the network star's fate. Rupert Murdoch, James's father and the company's chairman and majority shareholder, has been running Fox News since Ailes left. James's brother Lachlan is also chairman.

You could probably put a monkey in the seat and as long as it spouted appropriately conservative views there would be decent ratings.

Brian Wieser

The elder Murdoch, 86, is viewed as more politically in line with O'Reilly, a famously combative champion of the right-wing, than his son James. The 44-year-old CEO and his wife Kathryn founded Quadrivium, an organisation focused on promoting science, equal opportunities and environmental issues.

Risk to Sky

One of Fox's biggest investments since he took over as CEO was a $US725 million investment in National Geographic, acquiring its TV channels and magazine, and doubling the society's resources for investments in science, research and education. James views the National Geographic network, with its emphasis on nature and ecology, as an ideological counterweight to Fox News, where climate-change deniers are regularly featured, a person with knowledge of his thinking said.

Fox executives aren't prejudging the outcome of the Paul Weiss investigation into O'Reilly's actions, and all three Murdochs will reach a consensus about what to do when the probe concludes, said another person, who asked not to be identified discussing private information. Fox News and O'Reilly's attorney Mark Fabiani have said the anchor will return when his vacation ends.

The key risk for investors, Wieser said, is any impact on the ability of Fox to complete its acquisition of London-based Sky, which is being reviewed by regulators.

The UK has strict standards that require any owner of a broadcaster to pass certain thresholds to be considered "fit and proper" to hold a license. While accusations of discrimination at a company would not be enough to fail such a test, regulators could be concerned about an by US federal prosecutors into Fox's disclosures of legal settlements, said Claire Enders, founder of researcher Enders Analysis.

As a young CEO, James Murdoch should also be concerned about the aging demographic of the Fox News audience.

"Its extraordinarily important for someone of that age to move towards businesses that you can really manage in a more conventional way, which are also more global businesses," Enders said in a telephone interview. "One of his top concerns in pursuing the Sky transaction is to diminish the company's dependence on Fox News."