And that means that Real are concerned Chelsea will complicate negotiations due to how difficult it will be to sign a replacement.
Marca add that the club will not pay the reported £180million that Chelsea want for Hazard.
But, with the player having just two years on his current contract left to run, Real are still hopeful his future can be resolved.
Meanwhile, Belgium boss Roberto Martinez has urged Hazard to consider quitting Chelsea.
"It could be the best time [for Hazard] to try something different," Martinez told Spanish radio station Cadena Ser.
Chelsea transfer news: Real Madrid want Eden Hazard to fill the boots of Cristiano Ronaldo (Image: GETTY)
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Eden Hazard dances to chant during World Cup homecoming
"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.
"Players need new challenges and new projects. Perhaps it's a good time for [Chelsea] and for Eden [to split].
"I would be very surprised if Chelsea didn't have big offers for him right now."