The company, which is run by the Murdoch family, said in a statement: "Roger is at work. The review is ongoing. And the only agreement that is in place is his existing employment agreement."
The Fox vet has vehemently denied Carlson's charges, calling them outrageous and defamatory.
The magazine also reported that Rupert Murdoch and sons Lachlan and James had made up their minds that Ailes must go, despite Fox News Channel being a key revenue driver at the corporation.
Talk of the polarizing media titan's fate has lit up social media.
The maelstrom comes at a less than ideal time for Fox News, with the Republican National Convention in full swing in Cleveland.