Roger Ailes’ time at the helm of Fox News could be nearing its end, according to a new report Monday by New York magazine.

The report, by Gabriel Sherman, a longtime chronicler of the Fox News chief and his tenure at one of the nation’s most influential news outlets, said that Rupert Murdoch and his sons, James and Lachlan, had decided to remove the executive from his post in the wake of a sexual-harassment lawsuit leveled against him by former Fox News anchor Gretchen Carlson. The report, citing unnamed sources, suggested the executives, who run Fox News parent 21st Century Fox, were considering various strategies to have Ailes step down.

“This matter is not yet resolved and the review is not concluded,” 21st Century Fox said in a statement. A spokeswoman for Fox News could not be reached for immediate comment.

Carlson leveled allegations in a suit filed in Superior Court of New Jersey charging that the executive had propositioned her sexually and that she had suffered unfair treatment from Steve Doocy, her co-host for several years on “Fox & Friends,” the Fox News morning program. Carlson left the network in June. In a statement, Ailes said her charges were false and came in retaliation for her contact with Fox News not being renewed. Meanwhile, 21st Century Fox, the parent company of Fox News, said it would conduct an “internal review” into the charges made against both Ailes and Doocy.

The report comes after several employees of Fox News and Fox Business Network – both supervised by Ailes – have come forward to support him. Bill O’Reilly, Maria Bartiromo, Geraldo Rivera and several others are among the members of Fox News’ on air staff who have defended Ailes and the corporate culture he has put in place. Lawyers for Ailes have over the last week filed motions to have the case moved to arbitration, citing Carlson’s employment agreements with Fox News. Carlson’s suit was leveled at Ailes personally, but did not include Fox News.