The report in the tabloid paper goes onto say that the move could mean long-term Liverpool target Gundogan is now free to leave the Bundesliga giants.
Gundogan worked alongside Liverpool boss Jurgen Klopp at Dortmund for several seasons before Klopp left at the end of last season.
The 25-year-old admitted earlier this month week that he was considering his future.
“There is still no decision, and of course, everything has to be considered very carefully, because your career is limited in time,” Gundogan was quoted as saying by Goal.
“But to be honest, everything is still open.”
Gundogan has been linked with a move to Anfield since the appointment of Klopp as manager in place of Brendan Rodgers.
The Germany international is tied into a contract at Dortmund until 2017 after signing a contract extension at the start of the season.