The Spanish football website Fichajes states that the 25-year-old is interested in a move away from Dortmund despite their impressive run of form in the Bundesliga this season.
Gündoğan has been linked with a move to Anfield since the appointment of Jurgen Klopp as manager in place of Brendan Rodgers.
The report goes onto state that the 26-year-old has 18-months left on his contact with Dortmund and Liverpool will monitor his situation to determine if a move is possible.
The Bundesliga giants sit in second place in the league with 35 points in 15 games. Gündoğan has provided five assists and scored two goals in 25 appearances for Dortmund this season.