City are light up front after selling Carlos Tevez to Juventus, whilst Edin Dzeko may also leave this summer.
The Independent report that Gomez heads a list of targets including Pablo Osvaldo, Alvaro Negredo and Oscar Cardozo.
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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?