Werder Bremen hope to re-sign Per Mertesacker if Arsenal do not extend the defender's contract.
Mertesacker, 32, is in the final year of his current deal at Arsenal, and has been sidelined with cartilage damage in his knee since July.
The Gunners captain said this week he was open to a return to Germany should Arsenal decide against renewing his contract, and his first club, second-tier Hannover, have expressed an interest in his services.
However, Bremen would appear to be in a stronger position should they retain their top-tier status, and sporting director Frank Baumann, who played alongside Mertesacker from 2006 through to his retirement in 2009, told Bild he "can see Per at Werder."
Bild also reported that Bremen would offer Mertesacker a managerial training programme, and Baumann said discussions with the former Germany international had already taken place when the club signed Serge Gnabry from Arsenal.
"In the course of Serge's transfer, we also talked about his [Mertesacker's] future," Baumann said.
On Tuesday, Mertesacker had told kicker he was thinking about options for his future.
He said: "I ask myself what would make sense if things were to end at Arsenal. Where can I be of any help? What do I want? Could I maybe return to Germany?"
Mertesacker, who hopes to resume training next month, faces competition from Laurent Koscielny, Shkodran Mustafi, Gabriel Paulista and Rob Holding for a centre-back spot at the Emirates Stadium.