The BBC claim that City are set to confirm the transfer of the 25-year-old from Dortmund shortly. The report goes onto state that the transfer fee is in the region of £20 million.
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.
The Germany international was also sidelined for the 2014 World Cup with a back problem that ruled him out for almost the entire 2013-14 season.
Gundogan joined Dortmund from Nuremberg back in 2011 and helped them reach the 2013 Champions League final before signing a new contract in 2015 that still has a year to run.
The 25-year-old has seven assists and three goals in 40 appearances for Dortmund this season.