The Blues have turned their attention to the Spanish striker after missing out on Romelu Lukaku who opted to join Manchester United instead.
And with Antonio Conte telling Diego Costa he has no future at the club, Morata has emerged as the leading candidate to make a Stamford Bridge switch.
Spanish outlet Diario Gol report Real are ready to give up on Kylian Mbappe and put all their energy into bringing Hazard to the club instead.
Zinedine Zidane is a big fan of the Belgian and wants him at the Bernabeu this summer.
The reports claim Chelsea could be tempted in doing business with Real if they can secure the signing of Morata.
Real president Florentino Perez will try and convince Hazard a move to the Spanish champions is the right thing for his career.
The 26-year-old was in fine form for Chelsea last season as the Blues won the Premier League title in Antonio Conte’s first campaign in charge.
Real are convinced Hazard would be a superb signing as he has already proven himself at a top club in Europe.
Chelsea have signed two players so far in the current transfer window, goalkeeper Willy Caballero and defender Antonio Rudiger.
Real have today let James Rodriguez leave for Bayern Munich on a two-year loan deal opening a slot in their midfield.