Bale faces an uncertain future at the Bernabeu after struggling for form in recent months.
The rise to prominence of Marco Asensio has raised further questions about the Welshman’s long-term prospects with the Champions League winners.
According to Spanish news outlet Don Balon, Real Madrid president Florentino Perez has already drawn up a list of transfer targets ahead of next summer’s window.
Tottenham midfielder Dele Alli and a new goalkeeper are high on Perez’s wish list.
But Zidane has put in a request for the club to pursue a move for Hazard.
Real head coach Zidane reportedly believes Hazard is the ideal arrival to offset Bale’s potential departure.
The Belgian has developed into one of the world’s best players since joining Chelsea from Lille in 2012.
He has helped the Blues to two Premier League titles, one League Cup and the 2013 Europa League.
Chelsea are aware of Real’s interest in Hazard, who has three years left on his contract.
Don Balon claim Stamford Bridge chiefs are hoping to tie up fresh terms to scare off Zidane and co.
