The 24-year-old was signed to BVB's youth team in 2002, but moved to Rot Weiss Ahlen a year later before being repatriated in 2009.
Under coach Jurgen Klopp, Grosskreutz has won two Bundesliga titles and the DFB-Pokal, and while he stated the feeling he has for his current employers, he also left the door open for a move to Anfield.
"I love Borussia, but I cannot rule anything out," Grosskreutz told Sports Image. "It would be a dream to play for Liverpool at some point. England is a dream for any footballer."
Grosskreutz had stated in November that he would prefer a move to Arsenal, but he appears to have had a change of heart.
Dortmund face Werder Bremen in the first Bundesliga match of the season on August 24.