The Spanish giants are also aware that the Blues are interested in James Rodriguez.
Real Madrid boss Zinedine Zidane is reportedly a big fan of Hazard and the Belgian also admires the France legend.
Blues officials are confident incoming boss Antonio Conte can get the best out of the 25-year-old.
But a huge bid plus the offer of Morata could tempt Chelsea into doing business with the Champions League winners.
The Blues have already agreed a £33m deal for Hazard’s Belgium team-mate Michy Batshuayi, who has reportedly passed a medical as well.
But at Euro 2016 he has been impressive for Belgium, scoring in the last 16 victory over Hungary.
Morata remains a target for Chelsea after Real triggered the buyback option to re-sign him from Juventus for £23m.