The 24-year-old Argentine international recently turned down a new contract offer at the Santiago Bernabeu, and is looking to double his current wages of £40,000-a-week.
Di Maria has 27 caps and five goals at international level, but has struggled to consistently replicate his best form domestically, since moving to the Spanish capital from Benfica in 2010.
The South American star has shown glimpses of his potential though, and as a result is demanding parity with some of his senior teammates at Real.
The move will be seen by many as a bold one, as Di Maria challenges Jose Mourinho in his search for a bumper new deal, but Chelsea will be ready to offer him an escape-route if negotiations come to a head this summer.
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