According to MailOnline's Simon Jones, BVB want to extend his stay beyond his loan deal, which runs until the end of the season.
Dortmund secured him for the second half of the campaign last month as a replacement for Pierre-Emerick Aubameyang.
The Gabon striker joined Arsenal while Gunners forward Olivier Giroud replaced Batshuayi, with the three transfers forming a chain.
Dortmund chief executive Hans-Joachim Watzke revealed the German outfit pushed for a slightly different deal: "We tried our best to get a permanent option for Michy Batshuayi, but it was a no go for Chelsea. When [Blues owner] Roman Abramovich says 'no,' it is a 'no.'"
Batshuayi has already made a significant impact in a short time at Dortmund, per Squawka Football:
Along with his clinical play, football writer Stefan Buczko noted another way in which the 24-year-old has helped them in the final third:
He seems to be enjoying his move from a personal standpoint, too:
The Belgian had netted 12 goals for Chelsea in 1,160 minutes of play in the first half of the season, but Blues boss Antonio Conte has never appeared convinced by him since his arrival for £33 million in 2016.
Last year, Batshuayi was given just 702 minutes to prove himself on the pitch at Stamford Bridge. Despite his limited playing time, he mustered nine goals, including the strike that sealed the Premier League title for the Blues.
Batshuayi still has room for improvement in some areas of his game, such as his movement in attacking situations, but he's a prolific goalscorer, which counts for a lot.
Given his impressive record, the Blues would do well to keep hold of him upon his return, particularly if he continues to do well in the coming months.