Cohen ordered an internal investigation into the hit show after a string of controversies which saw it criticised by communications watchdog Ofcom for breaching broadcasting rules over a ''racial'' term used by Clarkson.
The regulator decided the comment, made by the star during the programme's Burma special screened in March, was offensive.
That came just three months after Clarkson was caught up in another racism row which prompted him to apologise and be given a final warning about his behaviour by the BBC.
In that incident, unaired footage from the programme came to light in which he appeared to use the n-word.
In a letter to The Guardian, Cohen said: "While Jeremy and I disagree on the language some have recently found very offensive, I do not think he or anyone on the Top Gear team are racist."
Cohen said it was "no secret" there had been "some significant issues" on the show recently and said he "instigated a health check...to ensure that there were no further issues".
The show - and Clarkson - have landed in trouble before. An episode filmed in India was criticised by Indian diplomats and the BBC had to apologise to the Mexican ambassador after remarks made by Clarkson and co-hosts James May and Richard Hammond.
Clarkson was criticised by mental health charities after he branded people who throw themselves under trains as ''selfish'' and was forced to apologise for telling BBC1's The One Show that striking workers should be shot.