The German publication says Dortmund have already found the man they want to replace last season's Bundesliga Golden Boot victor as they are ready to approach Chelsea to sign Batshuayi.
Bellamy offered a fascinating insight into Carroll but said he lacks the professionalism and dedication to succeed at an elite club like Chelsea and called his character into question.
There's no doubt that Andy Carroll can be a massive annoyance to defenders and is certainly a good player when on top form.
"In general play he's very hard to link with, doesn't see the game", Bellamy told The Debate. And I never seen an inch of that.
Carroll may be struggling in front of goal this season, but the 29-year-old's contributions elsewhere should not be undervalued.
They are fourth in the division, have a dynamic strike duo in Eden Hazard and Alvaro Morata, so just why on earth do Chelsea need another forward?
"He's a handful, but no I don't think he is (the answer for Chelsea)", Wise told The Debate.
"And Andy won't push him as far because he will only play a certain amount of games and I think you want a player who is really going to push Morata, score goals and put him under pressure".
Chelsea have played out their last three games as goalless stalemates before the penalty shootout win over Norwich City today and there has been prima facie evidence of fatigue from the display of their attackers.