The report states that the Premier League giants are in talks with the 25-year-old’s representatives and look to have beaten Juventus and Barcelona in the race.
The Citizens have already agreed a to appoint Pep Guardiola in place of Manuel Pellegrini next season and are expected to strengthen heavily over the summer transfer window.
Gundogan was heavily linked with a move away from Dortmund last summer but instead signed a one-year extension. The Germany international’s current deal expires in July 2017.
The 25-year-old has six assists and three goals in 32 appearances for Dortmund this season.
Gundogan career began at Nuremberg before moving to Dortmund for £4m in 2011.