Hazard has been heavily linked with the La Liga giants and described them as the “best club in the world” as he fuelled transfer talk in the summer.
Radio station Onda Madrid, cited by AS , say that Los Blancos are now ready to offer Hazard his dream move, and they have already agreed terms with the player.
The main stumbling block is reaching an agreement with Chelsea, who are determined to keep hold of their star man.
They are said to be demanding a hefty price tag of around £150m to try and deter the Spanish side, who are reportedly unwilling to pay such a big fee given Hazard’s contract at Stamford Bridge will expire in 2020.
A part-exchange deal involving Mateo Kovacic could provide a solution to that problem, with the Croatian midfielder keen to stay in West London when his current loan deal ends in the summer.
Chelsea are set to offer Hazard a huge new contract in a bid to keep him at Stamford Bridge.
Manager Maurizio Sarri addressed the issue this week, stating that they are ready to “immediately” agree a new deal.
“I want Eden here, of course,” said the Italian.
“But I want him here if he wants to stay here.
“The club is available to sign a new contract immediately, but it’s up to him if he wants to renew or not.
“I know very well that there are discussions between the club and the manager of Eden every week, I think.
“So if there is something new, the club will call me immediately.”