Ozil also said that he showed his professionalism during his spell there, which he hopes will stand him in good stead for his time at Arsenal.
"I don't want to say anything bad about Madrid," BBC Sport quotes Ozil as saying. "I had three wonderful years there, we achieved a lot and we won trophies.
"I had a great time there. People who know me know how professional I am. Over the years there I played 159 games. If you are not professional in your life I don't think you can play that many games.
I don't care about all the rumours, I have a new task now and I am looking ahead."
Ozil moved for a club-record £42.5m.