Batshuayi was brought in on-loan from Chelsea during the January transfer window, and since arriving the Belgian has been in sparkling form.
The striker has been involved in four goals in his first two Bundesliga games, and due to his brilliant start Dortmund are said to be ready to make a permanent move for the striker in the summer, as reported by the Evening Standard.
Dortmund chief executive Hans-Joachim Watzke recently spoke about the possibility of keeping the Belgian at the club beyond the end of the season and claimed that it would be difficult to keep the striker if he continues his record of scoring in every game.
"There is always a chance, although if he scores in every game, it will be difficult."
Batshuayi was brought in as a replacement for Pierre-Emerick Aubameyang who left during in January to join Arsenal. Despite letting their top goalscorer go die Schwarzgelben haven't missed the Gabon international and are in league terms in a better position - currently sitting third in the table.
With Chelsea currently in crisis on the pitch it may be a wise decision for Batshuayi to sign permanently at Dortmund - especially with the current uncertainty surrounding the future of Blues boss Antonio Conte.