The midfielder left the Spanish giants to join the Gunners in 2013 for a reported £42.5m fee, and after a slow start has become a key member of Arsene Wenger's team.
The German World Cup winner is in negotiations with Arsenal over a new deal but is yet to agree fresh terms, much like his teammate Alexis Sanchez.
According to Marca, Ozil regrets leaving Madrid and would be open to returning to the Bernabeu, where he won three trophies including the La Liga title in the 2011-12 campaign.
The 28-year-old, whose contract expires in 2018, is believed to have an admirer in Real president Florentino Perez.
Ozil has been influential for the Gunners this season, having scored seven goals in all competitions.