However, Chelsea want a nine-figure fee for their prized asset, even if it means running the risk of losing him for free next year.
Real are likely to heavily invest this summer, after a hard season following the departures of Cristiano Ronaldo and Zinedine Zidane.
The 28-year-old Belgian winger will soon enter the final year of his current contract.
According to The Mirror citing Telegraph report, Chelsea eggheads will demand over £87.5m the Los Blancos coughed out to sign Gareth Bale from Tottenham in 2013, by placing a £100m tag on Hazard. The European champions are now cash strapped as the majority of their funds have been diverted towards the renovation of Santiago Bernabéu stadium for a staggering £350 million.
He wants to leave from Russian Federation: agreement to sign a contract until 2023 (€4.5million per year). Chelsea in the meanwhile are looking at other targets which includes the Italian Gonzalo Higuain.
The Croatian is now on loan at Stamford Bridge and should Maurizio Sarri decide that he wants to keep him on a permanent deal, then Madrid could include him in any potential deal for Hazard.
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His team remain on one point following the goalless draw from their opening match against Palestine. "It's important to grow into the tournament".
Hazard was accused of being disrespectful following his performance for Chelsea against Newcastle.
Without the necessary the cash in the coffers, it would be a challenge to bring Hazard to Madrid.
Whether he is included in as part of a Hazard bid or a transfer is negotiated separately, Real will hope that Kovacic can help them cover the cost of any deal for Chelsea's star man.
"Real Madrid are still interested as far as I know, but they are still yet to make their move".
Eden Hazard has been linked with a move to the Spanish capital since the summer.