With just 18 months left to run in Hazard's current deal with the west London side, Chelsea have swiftly offered the Belgian forward a new contract that reportedly would make him the club's best-paid player.
La Liga giants Real Madrid have made it clear that they want to lure Hazard to the Santiago Bernabeu and will try again in the winter transfer window.
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.
The main stumbling block is reaching an agreement with Chelsea, who are determined to keep hold of their star man.
This rumour has been doing the rounds for a number of months now, with the Belgium worldwide edging worryingly closer to the end of his contract at Stamford Bridge.
The report claims that Los Blancos have agreed to pay €170m for the Belgian global at the end of the season, whilst Mateo Kovacic will also be included in the deal as he makes his loan deal a permanent one at Stamford Bridge. Subscribe to our SMS sports service by texting "SPORTS" to 22840.
In the meantime, Chelsea are working on a new deal for the Belgian something coach Maurizio Sarri alluded to when asked about Hazard's situation earlier this week.
"I want him here, of course, but I want him here if he wants to stay here", Sarri said in a press conference.
I know very well that there are discussions between the club and the manager of Eden every week, I think.
Long-term Chelsea target Daniele Rugani is poised to sign a new contract at Juventus.
"So if there is something new, the club will call me immediately".