The Germany midfielder has found it difficult to get regular first-team football at Signal Iduna Park, but he insists he wants to stay and fight for his place rather than leave
The 24-year-old has been linked with potential suitors in the Premier League, namely Liverpool, after losing his place in the first team under Jurgen Klopp this season.
But Grosskreutz insists he is determined not to leave the club, vowing that he will work tooth and nail to regain his spot in the XI rather than seek pastures new.
"I have no trouble with Borussia Dortmund and, basically, I don't want to leave," he told Sport Bild.
"I am not giving up just because I am not in the first team. Borussia Dortmund always were and still are my favourite club.
"Until now I have not been offered a new deal that I could sign straight away, but I am looking forward to receiving that kind of proposal."
The German winger has featured 14 times for BVB in the league and last played and scored in the 3-1 victory over Hoffenheim in December.
The Bundesliga holders return to action against Werder Bremen on January 19 but trail 12 points behind table-toppers Bayern Munich.