Chelsea owner Roman Abramovich faces a fight to keep Hazard, with Real Madrid determined to sign the Belgium international as a replacement for Cristiano Ronaldo.
Ronaldo jumped ship to Juventus earlier this month and, with Kylian Mbappe and Neymar out of reach, Real Madrid are eyeing a Blues raid.
Chelsea star Hazard has done little to dampen talk of a move to Real, regularly waxing lyrical about the La Liga giants.
But the Daily Mail say Chelsea expect Hazard to stay calm amid the speculation over his future.
It is claimed that he believes the 27-year-old will not agitate for a move, despite the fact he dreams of moving to the Bernabeu.
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In the past, Real have refused to pursue Hazard – despite the wishes of former boss Zinedine Zidane.
That was because of Ronaldo, who always insisted on being their talisman despite Gareth Bale, Karim Benzema, Luka Modric and Toni Kroos also being at the club.
The Daily Mail say now, though, Real are determined to land Hazard.
But Chelsea are keen to ward off potential suitors for their No 10 by demanding a huge £150million to let him go.
As well as Real Madrid, Barcelona have also been tipped to sign Hazard.
But the winger appears to have eyes only for Los Blancos, recently saying: “Does Real make me dream less without Zidane?
“Zidane is someone special, it’s true, but I think Real is everyone’s dream.
“Zidane or no Zidane, the white jersey [of Madrid] is special but the blue jersey [of Chelsea] suits me well so it does not bother me if I stay.
“For now, it’s the World Cup. As I have said at least 100 times, I am at Chelsea and for the moment nobody has made me an offer.”
Hazard has won the Premier League title twice since joining Chelsea from Lille in 2012.