Batshuayi scored twice on his debut in victory over FC Koln on Friday night. The Belgian is on-loan to the end of this season.
BILD says BVB rejected the option to sign Batshuayi outright this summer, due to Chelsea insisting on a buy-back clause also being included.
However, the door has been left open to Dortmund and they can freely negotiate with Chelsea about an outright deal.
But they also know if Batshuayi continues his form, his price will increase week by week.