And while they are determined to land Manchester United keeper David De Gea, their prime target is Chelsea wing ace Hazard.
Real have ramped up their attempts to lure the Belgian away from Stamford Bridge.
Madrid insiders have briefed there have been no fewer than three separate meetings this year between club representatives and Hazard’s entourage.
Real made it clear to the Belgian they are prepared to smash the world record by paying £100million to tempt him away from Stamford Bridge.
Hazard has been promised a role as Real’s advanced playmaker, operating in the hole between the normal front three of Cristiano Ronaldo, Karim Benzema and Gareth Bale.
It is understood that the conversations between Hazard’s representatives and Real have been extremely detailed with discussions of tactics and formations.
While Hazard has publicly maintained he is happy in London, Real believe he is ready to push for a move because of his respect for Zidane, whom he views as a footballing idol.
Chelsea is likely to rebuff the initial approach and is keen to keep Hazard on board for next season’s attempt to regain the Champions League they won in 2012.
But Antonio Conte is demanding significant funds for his proposed rebuilding effort over the summer as he completes a squad able to succeed both domestically and in Europe and Chelsea may be willing to consider cashing in if Real are prepared to go even higher.
Meanwhile, United rejected an initial £60m bid for De Gea but are braced for a second bid after the game against Juventus in Cardiff.