Clarkson has been criticised for jokes about Mexicans and other national groups during previous editions of Top Gear.
But Cohen revealed that Clarkson had rejected criticisms of his language when the pair had discussed the director of television's unhappiness with the presenter's behaviour.
"He doesn't see a problem with some of the language he has used," said Cohen. "He feels differently about it from me."
Cohen said he did not think it was appropriate for the hit show to be transferred from BBC2 to BBC1, in line with a similar move made by The Great British Bake Off.
Discussing the future of BBC2, Cohen said the channel would be broadcasting a series on the history of Black Britain and showing what he described as "Britain's first transgender comedy", called Boy Meets Girl.
In the Autumn, BBC2 will broadcast Castles in the Sky, a drama on the invention of radar, starring Eddie Izzard.
- Independent