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Attorneys from a New York-based firm were said to be investigating Ailes after a sexual-harassment lawsuit was filed earlier this month by former host Gretchen Carlson.
According to reporter Gabriel Sherman, who once authored a book critical of the Fox News boss, Kelly told attorneys investigating claims of sexual harassment that when she first started appearing on Fox News about a decade ago, Ailes made unwanted sexual advancements toward her.
Kelly is a rising star in the media industry and considered by many observers to be the future face of Fox News. She first joined the cable network as a legal correspondent before being offered her own show.
Tuesday's explosive report was published just one day after the outlet, citing sources, said Rupert Murdoch and his sons had decided to remove Ailes as Fox News chief.
Sherman reported, citing two sources, that 21st Century Fox gave Ailes an August 1 deadline to either resign or face being fired.
The report also said that Donald Trump, the presumptive Republican presidential nominee, had provided advice on strategy to the longtime Fox News CEO.
A Fox News spokesperson was not immediately available for comment, but the network's parent company, 21st Century Fox, released a statement Monday saying a review was still underway.