The Daily Mail claim that Gundogan is keen on the idea of playing under Pep Guardiola in the Premier League.
The report goes onto state that Gundogan turned down Dortmund’s offers of a contract extension and has one year remaining.
The 25-year-old came close to leaving the Bundesliga giants last summer but instead signed a one-year extension.
The 25-year-old has six assists and three goals in 32 appearances for Dortmund this season.
Gundogan’s career began at Nuremberg before moving to Dortmund for £4m in 2011.
Manchester City are currently in forth place in the Premier League following their 3-0 defeat at the hands of Liverpool on Wednesday.
Dortmund find themselves in second place, just five points behind league leaders Bayern Munich.