The Chelsea forward has emerged as a key target for the Santiago Bernabeu club and has delayed signing a new £300,000-a-week deal at Stamford Bridge as he fears it might stop a move.
Spanish outlet Diario Gol has now claimed that manager Zidane has been given permission by his president to sign Hazard.
Zidane himself is a long-standing admirer of the Belgium international and, as Sportsmail reported earlier this week, views him as key to his rebuilding project at Real.
A move for Hazard was put on the backburner due to the stunning form of Spanish youngsters Marco Asensio and Isco towards the end of last year.
But Real have stumbled in La Liga this campaign. They are fourth in the league, well behind leaders Barcelona, and only managed second place in their Champions League group.
And that means Perez is willing to sanction a move for Hazard, especially as Cristiano Ronaldo is now seen as less integral to their future.
Diario therefore has suggested that Zidane made contact with the 26-year-old forward this week after he delayed penning his new contract.
Last month, Hazard admitted it would be a 'dream' to play under Zidane. He said: 'Everyone knows the respect I have for Zidane as a player, but also as a manager. He was my idol.