The Germany international's representative has admitted that the English side are interested in his client, but they have not made a formal move to sign him
The English Premier League club see the 23-year-old as a potentially valuable addition to their squad, and the club's head scout, Steve Rowley, watched BVB's 1-0 Champions League win over Olympiakos.
Rowley is thought to have been impressed, but Grosskreutz's agent has stressed that Arsenal have yet to step up their interest.
"We are aware of the English interest in Kevin. However, there hasn't been any personal contact with Arsenal so far," Liolios was quoted as saying by Bild.
Grosskreutz, who joined Dortmund from Rot-Weiss Ahlen in the summer of 2009, recently admitted that he would be open to a move to the Premier League and labelled the north London side an "interesting option".
"If I would ever leave Dortmund, it would be for an English team. And a club like Arsenal are an interesting option for any player," he told Bild.
The attacking midfielder's contract with the Bundesliga champions runs until the summer of 2014.
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