The Manchester City striker previously played for Atletico Madrid, but could jump at the chance to join a big club like Real.
According to the Daily Star, Real Madrid are considering bidding as much as €50 million for the player.
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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.