The Premier League clubs are looking to sign the striker in a cut-price January deal, according to The People.
The 20-year-old is regarded as one of Spain’s hottest young talents and is also being linked with a move to Juventus.
Isco has four years left on his current contract at Malaga, but has a £16million buyout clause in his deal.
Malaga boss Manuel Pellegrini has admitted he expects Isco could leave the club.
He said: “He is a player who has a great future. Nobody knows what his limit is.”
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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.