Hazard recently suggested that he might be ready to 'try something different' after spending the last six years with Chelsea and hinted that Madrid is his preferred destination.
With the 27-year-old on the Bernabeu radar for several years, the timing could actually now be perfect as Real are in the market for a new marquee attacking player following the €100m departure of iconic talisman Cristiano Ronaldo to Juventus earlier this month.
In the latest update on the developing saga, Italian journalist Alfredo Pedulla has claimed that 'Real insists for Hazard', suggesting that the reigning European champions really want him.
Equally, however, Pedulla says 'Chelsea raises the price more and more'.
Real insists for Hazard, but Chelsea raises the price more and more— Alfredo Pedullà (@AlfredoPedulla) July 16, 2018
It has already been rumoured that the west London side would demand in excess of the world record €222m fee that took Neymar to Paris Saint-Germain last summer, with Pedulla's comment also consistent with recent speculation that Chelsea plan to reject offers.
Hazard has joined enjoyed a fine World Cup during which he captained Belgium to a third place finish, their best ever, and was himself awarded with the Silver Ball as the second best player at the tournament and Belgian coach Roberto Martinez has backed him for a new club challenge.
"It could be the best time to try something different," Martinez said of Hazard's situation on Spanish radio show 'El Laguero'.
"He is a player who has maturity and a lot of leadership. His play is based on talent.
"Hazard could carry a new project anywhere in the world. He is at the best moment of his career. He could fit in any team in the world."
Chelsea will begin the 2018/19 season under fresh management after sacking Antonio Conte and hiring Maurizio Sarri, but a dismal fifth place finish in the Premier League last term will see the club not competing in the Champions League for the second time in the three years.