Ozil, 22, moved to the Bernabeu last summer from Werder Bremen as Mourinho started to shape the team he felt could challenge for honours and the Germany international told Kicker magazine he reckons that time has now come.
He said: "Real Madrid have made a lot of signings in the last couple of years, but you can now tell we understand each other on the pitch.
"We are much stronger. We've taken a step further compared to the previous campaign. I want to win every title.
"We would have liked to win the Spanish Super Cup, but what matters is we can compete at a really high level."