Ozil, 23, has lost his place in the starting XI after the arrival of £33m playmaker Luka Modric this summer. However, Ozil returned to the first team in the 2-2 El Clasico draw against Barcelona and substituted 10 minutes from time for Brazilian Kaka.
But during the Champions League away win against Ajax, the 23-year-old was dropped after manager Jose Mourinho suggested that the midfielder 'lacks quality' with lack of form.
The former Werder Bremen star has been under fire since the start of the La Liga season which saw Real Madrid fall eight points below rivals Barcelona in seven games.
But the German star, who takes on Republic of Ireland this week, feels that he has nothing to prove to anyone and has no reason to leave the Bernabeu.
"When you play for Real Madrid you can not think of anything else," he said.
"I know nothing and I have no reason to leave," he added.
"I do not play football to prove something to someone, but because I enjoy football.
I don't have to prove anything to anyone."