The Germany international is confident that he will continue to be a key player at Santiago Bernabeu under Carlo Ancelotti after the Welshman's record transfer from Tottenham
Goal understands Spurs and Madrid have reached an agreement over an £86 million deal for the 24-year-old.
Ozil has made it clear that he will welcome the Welshman to the Santiago Bernabeu with open arms.
"At Real Madrid, we are happy with every player who strengthens the team. That's why I do not have any problems with the signing of Bale," the Germany international told Bild.
"There's always competition for places when you play at a big club like Real Madrid. I know how to deal with it. I will never leave a club due to the stiff competition for places.
"This is my fourth season at the club and I have always been a regular. I know exactly what I'm capable of. I feel the coach's faith and I have no doubt that I will be a regular again."
The 24-year-old then went on to discuss his long-term future at Madrid and stressed that he will at least stay at the Liga giants until the end of his current deal.
"I can guarantee that I will fulfil my contract until 2016 here," he said. "Obviously, I don't know what will happen after that."