The tabloid newspaper states that City have agreed a €30 million deal with the Bundesliga giants.
Bild goes onto say that Man City have also reached an agreement for a five year deal with Gundogan. The Germany international will earn €5 million per season at City.
The Sun newspaper 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.
The 25-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.