The Germany international joined the Spanish giants from Werder Bremen in the summer of 2010 and quickly developed into an important first-team member at the Santiago Bernabeu.
Ozil has been less impressive in the opening months of the 2011-12 campaign, but he is pleased to still have Zidane's support.
"I often speak with Zidane. He tells me all the time: 'Mesut, you know what you're capable of. Go out there on the pitch and play your own game, just do your own thing out there," Ozil was quoted as saying by Kicker.
The 23-year-old faces stiff competition from Brazil international Kaka for a starting berth, but he remains unperturbed by the current situation.
"Kaka is doing very well at the moment. So I don't play every single game. Jose Mourinho has explained that whoever is doing a good job is playing.
"We have a lot of big names in the team and they all want to play. I want the same thing, though. I am very happy to be part of this Madrid and want to stay put for many years."
Real Madrid are currently preparing for Wednesday's Champions League Group D match away against Olympique Lyonnais.
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