The challenge of playing in the Premier League appeals to the 24-year-old who has long-been linked with a move to Anfield and scouts from the club are expected to be at Dortmund's clash against Ajax in Amsterdam in the Champions League on Wednesday night.
Grosskreutz is said to be a close friend of Liverpool loanee Nuri Sahin and has hinted at a move to England at some point but, with his contract running out at the end of the season, he could be available for a knockdown fee in January.
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."
Liverpool last week