The report states that Dortmund are preparing for life without Gündoğan after lining up Radja Nainggolan as his replacement.
Dortmund are close to sealing a €35 million deal with AS Roma for the Belgium international.
However, Arsenal manager Arsene Wenger recently brushed off reports linking Arsenal with a January move for the Germany international.
“He’s not a defender. At the moment we are more looking for the defensive department,” Wenger responded when asked about Gundogan at a press conference last week.
Gündoğan’s contract expires in 2016 and Dortmund want to avoid losing Gündoğan on a free transfer.
The 24-year-old is understood to be available for around £20m.
Gündoğan was one of the central figures of the Dortmund side that reached the final of the UEFA Champions League in the 2012-13 season.
Gündoğan has scored on goal in 12 appearances for Dortmund this season.