The Djurgardens playmaker has already caught the eye of Premiership giants Liverpool, and was flattered to be linked with a move to Anfield.
The German sides have also been keen admirers of the 20-year-old and are now stepping up their interest in him.
Kallstrom has already earned nine caps for Sweden and is widely regarded as one of his country's top talents.
Both the German champions and rivals Rostock went to Sweden to watch the (question mark) million-rated star in action when he pulled the strings in a 4-0 mauling of Osters IF.
Dortmund are thought to be the keenest of the two sides and if Liverpool continue in their interest, they would be the only one of the two able to rival The Reds for Kallstrom's signature.