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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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?