The La Liga giants are determined to land Chelsea's star man this summer.
Zinedine Zidane wants to add another Galactico to his side in the next transfer window to work alongside Gareth Bale and Cristiano Ronaldo.
Eden Hazard has reportedly told his close friends that he wants to stay at Chelsea.
Eden Hazard could be on his way out of Chelsea this summer
Real Madrid have reportedly held positive talks with Eden Hazard
But Spanish newspaper Marca claim Madrid have held positive talks with Hazard's representatives over a potential move this summer.
Los Blancos president Florentino Perez has tracked the Belgium international since taking over the Spanish giants in 2012.
And Zidane reportedly wanted to sign Hazard last summer, but a deal never materialised.
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Zinedine Zidane is intent on bringing Eden Hazard to Real Madrid
Antonio Conte is said to be interested in signing James Rodriguez, and the report in Marca claims any deal for him could aid Madrid's hopes of signing Hazard.
Hazard's current deal at Chelsea doesn't end until 2020 after signing a five-and-a-half year contract in February 2015.
Madrid were initially handed a transfer ban in September last year that would see them unable to sign any players in 2017.
But that was later cut to just the January transfer window meaning they can bring in new recruits this summer.