The Belgian joined the German club on loan during the January transfer window and hit the ground running with five goals in his first three games.
Dortmund are now eyeing up signing the 24-year-old permanently in the summer but
a deal will not be straightforward.
The Bundesliga giants wanted an option-to- buy clause as part of the loan deal for Batshuayi, but Chelsea snubbed that request.
That means Dortmund will have to reopen talks in the summer if they want to sign the striker and, given his form, the Blues will
demand a big fee.
However, according to Bild, Dortmund are hoping they could get the upper hand in negotiations if Batshuayi demands to join them.
The Belgian appears very settled at his new on-loan club and BVB feel that he would elect to join them over anyone else.
That would prevent Chelsea from ramping up a bidding war by allowing other clubs to make approaches.
Dortmund are reportedly willing to spend around £50million on Batshuayi, who cost Chelsea £33million in 2016.
And it appears Dortmund have been boosted in their pursuit after Batshuayi hit back at Chelsea over their treatment of him and said he feels ‘trusted’ at the Westfalenstadion