The Germany international has been linked with a move to Anfield ever since the arrival of Jurgen Klopp.
“This is an issue that is always floating around,” Gündoğan was quoted as saying by Goal when asked about a potential switch to Liverpool.
“I am very happy with BVB and feel very comfortable here.
“Of course, I can imagine remaining here beyond the end of the season.”
Klopp has been appointed as the Liverpool manager on a three-year contract in place of Brendan Rodgers.
Dortmund rejected an approach from United just before the end of the summer window for Gündoğan according to the German newspaper Express.
Klopp won two Bundesliga titles and finished the 2012-13 Champions League as runners-up during his time in charge of Dortmund.
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 20 points in nine games.