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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.