The Times have reported that the Citizens have tabled an offer for the Germany international however, the newspaper go into state that Dortmund are likely to turn down City’s initial bid.
The Sun newspaper recently reported 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 expected to make major changes to their squad over the summer following the arrivals of Guardiola.
Gundogan has seven assist and three goals in 40 appearances for Dortmund this season. The 25-year-old has one year remaining on his current deal with Dortmund.
The Bundesliga side are are in second place behind leaders Bayern Munich with 74 points in 31 games. Dortmund take on Wolfsburg in the Bundesliga this weekend.