The Belgian's contract runs until 2020 and he could renew his deal with the Blues.
Hazard, who joined Chelsea for £32 million from Ligue 1 outfit Lille in 2012, has spoken often about the dilemma he faces in re-signing for the Blues or taking his chances at Real. I think the club is available to sign a new contract immediately, but it's up to him if he wants to renew or not.
"I want Eden here, of course". Now on loan in West London from Los Blancos, Kovacic doesn't want to return to the Bernabéu when his temporary Chelsea deal ends in the summer, and the six-time English champions would like the Croatian midfielder to stay on.
But Sky Sports News understands Chelsea have made Hazard a huge offer to be the club's highest earner and they are not commenting on reports his wages could rise towards the £300,000-per-week mark.
"So if there is something new, the club will call me immediately".
However, reports in the United Kingdom say Chelsea's policy of only handing one-year contracts to players over 30 - Hazard reaches the milestone just over six months after his current agreement expires - could prove a stumbling block.