Dortmund have been reluctant to let go of their star man whose contract comes to an end in 2016.
The Bundesliga outfit have reportedly offered a contract extension until 2019 worth €6.5 million per-season.
Dortmund are expected to cash out in the summer if Gündoğan rejects their contract deal to avoid losing the 24-year-old on a free transfer the following season.
The Germany international is keen on a move to the Premier League giants according to Sport Bild.
Gündoğan missed a large part of the season due to injury but has since recovered and returned to the starting lineup.
The 24-year-old has four assists and two goals in 22 appearances for Dortmund this season.
Gündoğan was born in the German city of Gelsenkirchen into a Turkish family.