The daily Manchester based paper states that City are close to signing the Germany international on a €26 million deal.
The report goes onto say that the deal is expected to be concluded this week with the midfielder already having agreed personal terms with City.
However, the north London based club have turned instead their attentions towards the Switzerland international Granit Xhaka.
Gundogan will miss Euro 2016 after dislocating his knee during training earlier this month. The German tabloid Bild report that it will take Gundogan four to six months for him to make a full recovery.
Gundogan has seven assists and three goals in 40 appearances for Dortmund this season.