Fox owner Rupert Murdoch and his sons James and Lachlan agree that Fox News Channel boss Roger Ailes should leave the company, but have not settled on the timing, New York magazine has reported, citing anonymous sources.
Former Fox News anchor Gretchen Carlson has sued Ailes, claiming sexual harassment. Ailes has denied the charges.
Fox hired the law firm of Paul, Weiss, Rifkind, Wharton & Garrison to conduct an internal investigation.
A lawyer for Ailes and representatives of Fox News and the Murdochs did not immediately respond to requests for comment.
Two sources briefed on the investigation told New York magazine that all three Murdochs "have settled on removing" the 76-year-old Ailes.
Lachlan Murdoch is executive co-chairman of 21st Century Fox and James Murdoch is chief executive officer.
After reviewing the initial findings of the Paul, Weiss investigation, James Murdoch "is said to be arguing that Ailes should be presented with a choice this week to resign or face being fired", the magazine said.
Lachlan "is more aligned with their father, who thinks that no action should be taken until after the GOP convention this week", the magazine reported.