BILD says Ozil would jump at the chance to return to Real should they make an approach.
Arsenal are aware of the German's opinion, which has forced them to up their offer to the player's camp.
With Ozil's deal due to expire in 2018, Arsenal are willing to make him the highest paid in the club's history - worth €230,000-a-week. The new agreement would extend to 2021.
Ozil had three years at Real before being sold to Arsenal for €50 million.