The 25-year-old is close to agreeing a £90,000 per week deal with the Sky Blues according to Goal.
Dutch newspaper De Telegraaf uploaded a photo of City chief Txixi Begiristain and Gundogan’s uncle and agent Ilhan Gundogan in Amsterdam.
Guardiola also met up with Begiristain in Amsterdam earlier this week to discuss the future of City, including potential transfer targets.
Gundogan was heavily linked with a move away from Dortmund last summer but instead signed a one-year extension. The Germany international’s current deal expires in July 2017.
The 25-year-old has six assists and three goals in 32 appearances for Dortmund this season.
Gundogan career began at Nuremberg before moving to Dortmund for £4m in 2011.