Dzeko is ready to leave City in January in order to secure regular first team football.
The Daily Mail reports that Dortmund are keen on the 27-year-old, but do not want to spend more than £15million for a replacement for Bayern Munich-bound forward Robert Lewandowski.
The German side look to strengthen in January as they looks set to lose several players this summer, including the likes of Lewandowski, Marco Reus and Ilkay Gundogan.
Reus and Gundogan have been strongly linked with a move to Manchester United.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?