The Germany international’s contract at the Emirates Stadium expires next summer and his future remains uncertain.
Ozil has recently been linked with a potential January transfer to Barcelona or Manchester United, and now his former team Schalke are showing an interest, even if they accept a deal in the short term is unlikely.
“I can imagine a return quite well," Tonnies told Kicker. "If there would be a possibility we would think about it.
"His return would be a nice story. But it won’t happen next summer."
Ozil arrived at Schalke in 2005 aged 16 and made his first-team debut a year later before leaving in 2008 to join Werder Bremen.
After a three-year stint with Real Madrid, Arsenal signed Ozil in 2013 for £42 million.
He produced an inspired display in the 2-0 derby win over Tottenham Hotspur on Saturday and afterwards Arsenal manager Arsene Wenger praised Ozil for his defensive effort and insisted his playmaker wants to stay in North London.
“The quality of the contract has to be good, I'm convinced they love the club, they love the team,” Wenger said about Ozil and team-mate Alexis Sanchez.
"I believe they want to stay but other top clubs are out there, who offer good contracts as well."