Rumours of a move were fuelled at the weekend when Ozil stormed down the tunnel after being substituted during Real's 1-0 win at Granada, but the 24-year-old says he will be staying in Spain.
Speaking at a shirt signing event the Germany international said: "I have a contract until 2016, I feel very good here and get on well with my team-mates.
"For me it's an honour to play here with this team.
"There has been a lot written in the press, they have spoken of interesting options but I have a contract and I am staying at Real Madrid."
Ozil had reportedly been unsettled by the arrival of Isco and Real's potential purchase of Gareth Bale which would leave his place in the side in doubt.
But the former Werder Bremen player says he understands the role that new coach Carlo Ancelotti wants him to play this season.
"I have the confidence of the coach and there is a series of objectives that we want to achieve in which everyone has their own role to play. This is one of the reasons I want to stay," he added.