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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.