Arsenal signed Pierre-Emerick Aubameyang – who Dortmund said they would only sell if a replacement was found – later on Wednesday.
Chelsea could sign Olivier Giroud from the Gunners as a replacement for Batshuayi to complete a three-way deal.
The German transfer window closes at 17:00 GMT on Wednesday.
Blues manager Antonio Conte said earlier in the week that the 23-year-old was in contention to play in their Premier League match against Bournemouth on Wednesday (19:45 GMT kick-off).
The Stamford Bridge club have also held talks with Tottenham over a possible swap deal involving Spurs’ Spanish forward Fernando Llorente – but Batshuayi rejected the move as he wanted to be a first-choice striker.
Dortmund travel to Koln for their next Bundesliga match on 2 February.