Ozil has been a revelation in La Liga since moving from Werder Bremen in 2010, but recent reports suggest the Germany international is unhappy that he rarely plays a full match, despite being a first-team regular under Jose Mourinho.
This has led to speculation that Liverpool are interested in his services, although the 23-year-old has moved swiftly to deny these rumours.
"I play in Madrid and I am very happy there," Ozil told DHA.
"I do not want to say anything else."
The classy midfielder did admit he was happy playing alongside Turkish pair Nuri Sahin and Hamit Altintop, who both, like Ozil, came from the Bundesliga.
"We are very good friends," Ozil added. "I already knew them from Germany. Now they are playing with me in Madrid.
"I am very glad to be playing in the same as them. Nuri also scored his first goal [against Ponferradina on Tuesday], I'm so glad."
Like Sahin and Altintop, Ozil is also of Turkish ethnicity, but chose to represent the German national team.