According to the London Evening Standard, Mourinho wants to use a portion of the £48m received for Luiz on the signing of France international Varane, who he gave a professional debut to while managing at the Bernabeu. The Portuguese coach has already hailed the 21-year-old as the best young defender in the world and is keen to bring him to west London despite the signing of Kurt Zouma and the emergence of Tomas Kalas.
Varane is currently focused on the World Cup and subsequently refused to talk about speculation regarding a move to Chelsea at the weekend, but the impressive form of Pepe and Sergio Ramos - plus a succession of untimely injuries - means there is a chance the young Frenchman could consider a move to reunite with his former boss in England.
Although Mourinho fell out with many of his players in his final season at Real Madrid, it's not believed that Varane is one of those with any ill-feeling towards the current Chelsea boss.
Club captain John Terry has signed a one-year contract extension, but the former England skipper is only expected to spend one more season at Stamford Bridge, paving the way for Varane to succeed the talismanic centre-back.
However, a series of impressive performances in Brazil this month will convince Real Madrid boss Carlo Ancelotti and other powerful figures at the Bernabeu that Varane is an indispensable member of the current Los Blancos' squad.