Los Blancos have made signing the Belgian their number one priority this summer and have already made the player a contract offer worth €15m.
It is understood that the Blues are demanding €150m, however, Florentino Perez is looking to sign the 27-year-old for a lower fee.
Following the conclusion of the World Cup, the Belgian revealed that he could go in search of a new challenge away from Chelsea, alerting Real Madrid to make their move.
“After 6 wonderful years at Chelsea it might be time to discover something different. Certainly after this World Cup.
“I can decide if I want to stay or go, but Chelsea will make the final decision – if they want to let me go.
“You know my preferred destination.”
His ‘preferred destination’ is understood to be Real Madrid, despite Barcelona also attempting to land his signature.
Madrid have already begun negotiations with the West London club over a move; with talks also being held regarding a deal for goalkeeper Thibaut Courtois.
The reigning European champions have already had an offer knocked back by the Blues, however, they are expected to return, having offered the player a very lucrative contract.
Hazard’s verbal agreement.
Hazard has already reached a verbal agreement with Real Madrid over joining the club, according to RMC.
The Belgian has also made joining the 13-time European champions his priority this summer and is expected to force through a move.
Hazard is top of the list of names Madrid have identified to replace Cristiano Ronaldo who joined Juventus earlier this month.