Ozil came through the ranks at Schalke before joining Werder Bremen after just 39 first-team appearances, refusing to sign a new contract and falling out with the club's management before his departure.
The 29-year-old is once again coming towards the end of his current contract with Arsenal, although the head of Schalke's supervisory board Clemens Tonnies ruled out the possibility of a reunion happening next season.
"I still have a great relationship with Mesut. We would definitely consider [a return]. If it fits for both sides, it would be nice," Tonnies told Kicker.
"The player could say that he returns to his roots, and that he plays football in this stadium and for those fans and the region once again. But it will certainly not happen next season."