The Blues, who are reeling from their Champions League exit, are long-term admirers of the Real Madrid centre half.
This comes amid a report that Chelsea are in talks over a new four-year deal for Mourinho and it is thought he could be handed a £75million transfer budget.
According to the Daily Mirror, Mourinho privately acknowledges that he needs to strengthen his defence.
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Raphael Varane is Chelsea's top target
Varane, 21, is thought to be his top target but would command a transfer fee of around £30m.
His chances of landing him are helped by the fact he has slipped behind Pepe and Sergio Ramos in the pecking order.
Chelsea already have Kurt Zouma at their disposal, but Varane would represent a big coup if they could sign him.
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