Dzeko has failed to make an impact at City since joining the club from Wolfsburg in January.
The Sun reports that Real Madrid boss Jose Mourinho is ready to make a £20million bid for the striker who joined City for £27million in January.
Dzeko signed a four-and-a-half-year deal when he joined City in January.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?