The report claims that City director of football Txiki Begiristain and Pep Guardiola have managed to convince the Germany international of Turkish origin to join the club after weeks of talks.
City are set to make an announcement regarding the transfer at the end of the season.
The 24-year-old midfielder was closely linked with a move to the Premier League last summer but the move stalled due to his unrealistic wage demands from his agent.
Gundogan currently has one-year remanning on his contract with Dortmund which expires in June but he is reported to have refused to sign a new deal in order to push through a summer transfer.
The Reds manager Jurgen Klopp does of course know Gundogan well from his time in charge of Dortmund in fact he is credited with making him the player he is today.
Premier League rivals Arsenal and Italian champions Juventus are also reported to be in the race for Dortmund midfielder.