Hazard is under contract at Stamford Bridge until the summer of 2020, and Chelsea risk losing him as a free agent this summer if no new deal is agreed.
All previous talks have failed to yield an agreement over an extension, but French outlet Le10Sport now claims that negotiations have started up again.
It is noted that Real are yet to make an offer of their own, but the situation has so far allowed Los Blancos to bide their time. The only club who need to act with urgency is Chelsea.
The importance of getting Hazard to commit his future to Chelsea has taken extra significant in the last week, after the Premier League club were hit with a two-window transfer ban by FIFA relating to 29 breaches of the rules on signing youth players.
Chelsea plan to appeal, although the ban will still have huge implications if upheld. It would not stop Hazard, or others, leaving the club, but would prevent them signing replacements.
There had been rumours earlier this year that Real were willing to shelve their reported long-standing interest in Hazard in favour of pursuing a world record deal for Neymar.
But the latest on that subject from Paris Saint-Germain president Nasser Al-Khelaifi resulted in further complete denial that the Brazilian superstar is for sale.
"Neither Real Madrid, nor any other club in the world, needs to call us about Neymar or any other player. Real Madrid know perfectly well that Neymar is not for sale and that the player won't leave PSG this summer," he said this week.
"We have a fantastic relationship with Neymar and his father and it is built to last a long time."
For Real, Hazard would still be the much easier target.
Source : 90min