Italian website Calcio Mercato, as quoted by The Sun, is reporting that the Blues have already turned down a £107m offer for the Belgium global from the Champions League winners.
Madrid has always been touted as the likely next destination for Hazard and Real's president Florentino Perez had apparently earmarked the 27-year-old as the replacement for Cristiano Ronaldo, who departed the Bernabeu for Juventus earlier this summer.
Courtois has so far rejected Chelsea's offers of a new contract, and is keen on a return to Madrid to be closer to his family.
Chelsea winger Eden Hazard is believed to be Los Blancos' main target for this transfer window after Cristiano Ronaldo's recent move to Juventus.
Comments made by the pair recently suggested they had a foot on a plane headed for Real Madrid and Sarri faces a tall order to retain their services going forward.
Who are Chelsea most likely to sign this summer?
Roman Abramovich may be operating from afar these days, but he has already backed his new man in the dugout with the £50million signing of Jorginho, stealing the midfielder from under Manchester City's noses.
He asked Abramovich to let him go to another club. "I don't want to talk about it and not interested in it".
"I would like to look at them in the eye and see what is best".
He said: "I have to say sorry to everybody because my English is not so good".
"If he decides to go to Chelsea for the reasons he has explained or will explain, then all the best for him".
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