The 26 year-old has been in outstanding form this season, scoring a huge 18 goals in his 17 Bundesliga appearances, and is attracting interest from a host of top clubs.
Barcelona have been linked with a possible move, with their transfer ban having ended this week, but it is the Gunners who are said to be in talks over a potential deal.
The BVB are said to have slapped a £42 Million price-tag on his head, which Arsenal appear willing to pay, in order to bolster their attack on the Premier League title.
The North-London side sit on top of the English top division at present, and will be keen to bring in some competition to Olivier Giroud and the injury-prone Theo Walcott up front.
Liverpool are said to be looking to rival any move made by the league leaders, with Jurgen Klopp having managed the forward previously.