Fox News is preparing to cut ties with star anchor Bill O’Reilly, according to people close to the situation, after revelations that he and Fox parent 21st Century Fox settled multiple sexual harassment complaints led to an exodus of advertisers from his show and mounting pressure on the network.

A final resolution on the fate of Mr. O’Reilly, host of the “The O’Reilly Factor,” could come as early as the next several days, the people said.

21st Century Fox, which will hold a board meeting Thursday, hasn’t finalized an exit agreement with Mr. O’Reilly, the people close to the situation said.

Related Video BMW and Allstate have joined numerous marketers who have pulled advertising from Fox News's "The O'Reilly Factor" after 21st Century Fox and its host, Bill O'Reilly, paid $13 million to settle sexual harassment suits. Photo: AP

Since an April 1 article in the New York Times detailing $13 million in settlements paid to five women who worked on or appeared on Mr. O’Reilly’s program, pressure has been growing on Fox News, both internally and from activists, to remove him.

Mr. O’Reilly has denied any wrongdoing, saying he paid settlements to “put to rest any controversies to spare my children.”

On Tuesday, an attorney for Mr. O’Reilly said the host has “been subjected to a brutal campaign of character assassination that is unprecedented in post-McCarthyist America” and added that he has “evidence that the smear campaign is being orchestrated by far-left organizations bent on destroying O’Reilly and Fox News for political and financial reasons.”

Fox News-parent 21st Century Fox and Wall Street Journal-parent News Corp share common ownership.

Mr. O’Reilly’s exit would be a stunning fall for a titan of cable news and would leave a prominent hole in the network’s prime-time lineup of conservative commentators. Fox News already had to replace another star early this year, Megyn Kelly, when she departed for NBC News. Her successor, Tucker Carlson, has fared well.

But filling Mr. O’Reilly’s shoes will be especially difficult: His show draws some 4 million viewers a night and is consistently among the highest rated programs across all of cable. Mr. O’Reilly, 67 years old, recently renewed his contract with Fox News at a salary of more than $20 million annually, people familiar with the matter said.

Initially, Fox News and parent 21st Century Fox stood by their highly-rated host. However, as advertisers fled the O’Reilly program, internal debate ensued over the pros and cons of keeping Mr. O’Reilly on the air. Since the Times published its initial report, dozens of advertisers have pulled out of “The O’Reilly Factor,” many of them shifting their ad buys to other programs on Fox News.

Mr. O’Reilly hasn’t been on the air since April 11, when he ended his show by announcing plans for a vacation. While Mr. O’Reilly had planned to take this week off, the early start to his vacation wasn’t part of the original plan, people familiar with the matter said. The plan was for him to return to his show next Monday.

Mr. O’Reilly’s camp said that the advertiser boycott was being driven in large part by liberal media watchdog group Media Matters and Mary Pat Bonner, a fundraiser with ties to Hillary Clinton. Ms. Bonner couldn’t be reached for comment.

There were other pressure points on advertisers. Some social media users were attempting to embarrass companies that were airing ads on Mr. O’Reilly’s show, and several media outlets were calling advertisers to ask what their stance was on the matter.

The drama surrounding Mr. O’Reilly follows the exit last year of Fox News Chairman and chief executive Roger Ailes, which put a spotlight on the treatment of women at the network. Mr. Ailes resigned in July after he was accused of sexual harassment by multiple women, prompting an internal investigation at the company. Mr. Ailes has denied all of the accusations.

21st Century Fox is being investigated by federal prosecutors, who are probing whether the company made insufficient disclosures about settlements of harassment claims, according to people familiar with the matter.

21st Century Fox said in a November regulatory filing that it made payments of $35 million during the quarter ending Sept. 30 to settle complaints or potential complaints related to Mr. Ailes. The settlements of interest to the investigation by the U.S. attorney’s office for the Southern District of New York predate those disclosed by the company in November.

The company has said it is cooperating with the investigation.

Initially, insiders at Fox News and 21st Century Fox thought the revelations about Mr. O’Reilly’s settlements would fizzle out after a day or so. However, a drumbeat of protests about Mr. O’Reilly’s alleged behavior, along with new allegations of harassment and the advertiser pullout, kept the heat on.

The law firm of Paul, Weiss, Rifkind, Wharton & Garrison LLP, which 21st Century Fox retained to help with the Ailes matter, was brought in again to look into some of the allegations against Mr. O’Reilly.

Some employees in senior positions at the company have felt it was important for 21st Century Fox and its senior management team—including Co-Chairman Rupert Murdoch and his sons, Co-Chairman Lachlan and Chief Executive James—to send a message regarding Mr. O’Reilly’s alleged conduct to the women of the company, top executives said. Rupert Murdoch took over as chief executive of Fox News after Mr. Ailes’s departure.

High-level discussions have commenced about Mr. O’Reilly’s dismissal and top executives were leaning heavily in that direction, the people said.

Meanwhile, 21st Century Fox is trying to win regulatory approval in the U.K. to acquire the portion of British TV giant Sky PLC that it doesn’t already own for $14.5 billion. High-profile critics of the deal have seized on the widening sexual-harassment scandal at Fox News in the U.S. as a reason to urge regulators to take a closer look at the overall company’s corporate culture in their review.

Write to Joe Flint at joe.flint@wsj.com