The 24-year-old German international has been heavily linked with a move away from the Bundesliga, with fresh speculation surfacing following his latest comments about an interest in England.
"Should I continue with my career in a foreign country at some point, the Premier League of England would be my top priority," he told Bild. "I really like the way football is played over there."
Grosskreutz is under contract with Dortmund until 2014, but that hasn't prevented rumours of a move to Anfield, reuniting him with friend, and Liverpool loanee Nuri Sahin on Merseyside.
Reds boss Brendan Rodgers is in the market for attacking reinforcements in January, and according to reports he is poised to send scouts to run the rule over Grosskreutz in tonight's Champions League clash against Ajax in Amsterdam.
The winger has recently forced his way back into Jurgen Klopp's starting line-up, and has appeared in 11 league games for Dortmund this season, as well as making three Champions League appearances.
Still considered as an important part of the Bundesliga champions' project, Grosskreutz is not thought to be forcing a move, and would be happy to pen a contract extension, if an offer is put on the table.
"I have no concrete thoughts on [a transfer] that," he added. "In terms of contracts, my first conversation will be Borussia Dortmund."