While the Germany international left Madrid for the Gunners on transfer deadline day, Mourinho parted company with the Spanish giants to return to Chelsea over the summer.
"Yes, we're in touch," he told Bild. "Jose sent me a message saying 'welcome to London'.
"What else have we said? That's between us. I've completely disconnected from Real Madrid.
"At 24 years of age I've played in Germany, Spain and England, the three best leagues in the world. I've been successful in all three, I'm a true European."
Ozil won La Liga and the Copa del Rey once each during his three years at Madrid.