According to Metro citing UK Sun, Hazard was eager to seal a move to the Los Blancos after last year's summer World Cup in Russian Federation, but club boss Maurizio Sarri talked him into accepting one more season at Stamford Bridge.
The Belgium worldwide on the Blues' books is considered to form part of world football's elite, as his consistency across many years has cemented a standing alongside the very best players on the planet.
The Sun report further claim that The Blues have rejected an opening bid of around £68m and this has left Hazard's representatives furious.
The Blues recorded a 1-1 draw away to Eintracht Frankfurt in the first leg of their Europa League semi-final on Thursday and they are hoping to defend fourth place in the Premier League with two rounds remaining.
The Belgium worldwide is in the final leg of his deal at Chelsea and will not pen an extension if they want to keep him against his wishes.
Hazard is seen as the player to spark this Real Madrid team into life, especially with the departure of Cristiano Ronaldo having left a huge shortfall in terms of goals and chances.
He has spent this season on loan at Cercle Brugge and Chelsea confirmed in a statement that the 23-year-old will make that move permanent in the summer.
Once they rolled out their new kit it got people talking including an Arsenal fan who said: "Chelsea's new home kit literally looks like a bus seat". But the move never materialized.
Sunsport understands Chelsea chiefs promised the Belgian last summer that he could leave for La Liga if he stayed for one more year.