The daily newspaper state that the Red’s can secure the services f the 25-year-old for approximately £17.6 million.
The highly rated midfielder has been linked with a move to Liverpool ever since the arrival of Jurgen Klopp last month.
The sports website states that Barcelona – who were linked with Gündoğan over the summer transfer window – are also keeping tabs on the situation.
Gündoğan recently played down reports linking him with a move away from Borussia Dortmund but opted not to rule them out completely.
“About my future? I currently have no idea. This is very, very far away,” Gündoğan told Sport1.
Gündoğan has started the season well in the Bundesliga under Dortmund’s new manager Thomas Tuchel. Dortmund sit in second place in the Bundesliga with 23 points in ten games.