The Times newspaper have reported that the City Blues are in talks with the Bundesliga giants and want the transfer wrapped up before the end of the season.
The report goes onto state that City are offering an initial £14million with another £3.8m depending on performances.
However, the Sun newspaper have 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.
Gundogan has seven assist and three goals in 40 appearances for Dortmund this season. The Bundesliga side are are in second place behind leaders Bayern Munich with 74 points in 31 games.