Batshuayi has scored five goals in three games so far, including two in their Europa League tie against Atalanta midweek, and Dortmund have already seen enough to chase a permanent deal.
Chelsea were not open to the idea of selling him in January, but their interest in Dortmund winger Christian Pulisic could change things.
The American is one of Europe's hottest talents, still only 19 years old, and he has expressed a desire to move to the Premier League before.
He would command a large fee, and Chelsea would be looking at a cash plus player deal to land his signature, with Batshuayi the perfect bargaining chip. Although rivals Liverpool and Arsenal are also rumoured to be interested.