The 25-year-old has a year remaining on his current deal with the Bundesliga giants and ESPN report that they are unwilling to offer Gundogan a new contract while he is injured.
The Germany international dislocated his knee during training earlier this month and will miss Euro 2016.
“We will postpone the plans until he is more or less recovered,” the Dortmund chief Hans-Joachim Watzke was quoted as saying by ESPN.
Gundogan had been a priority target for the incoming City boss Pep Guardiola before the injury, especially considering his current deal with Dortmund expires in 2017.
Gundogan’s fitness has been under scrutiny after the 25-year-old missed a year of football due to a back injury.
Gundogan has seven assists and three goals in 40 appearances for Dortmund this season.