Last season's Premier League champions are looking to tie their star man down to fresh terms as soon as possible and are willing to pay him as much as £300,000 per week.
It would make him the highest paid player in the club’s history, but Hazard isn't ready to commit the rest of his career to Chelsea just yet.
The news will come as a welcome boost for Real Madrid who, as well as monitoring Raheem Sterling's situation at Manchester City, are keeping tabs on Hazard's position.
'Los Blancos' are planning a squad overhaul next summer and will look to bring in a number of stars, including Hazard, in order to bolster their squad.