The 24-year-old has long been linked with a move to Anfield and scouts are expected to watch Wednesday's UEFA Champions League match against Ajax in Amsterdam.
Germany international Grosskreutz, a friend of Liverpool loanee Nuri Sahin, is under contract with Dortmund until the end of next season but he has hinted at a move to England.
He is quoted as saying in Bild: "Should I continue with my career in a foreign country at some point, the Premier League of England would be my top priority.
"I really like the way football is played over there. I have no concrete thoughts on that. In terms of contracts, my first conversation will be Borussia Dortmund."