The Mexican is on Madrid’s list of summer priorities up front along with Radamel Falcao, according to the Daily Mirror.
Hernandez has struggled for regular playing time with Robin van Persie arriving last summer from Arsenal.
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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.