The Belgium winger hinted that he would potentially be interested in speaking to Real if a bid was tabled, but was adamant that he will not decide where his future lies until he learns whether manager Antonio Conte will still be at Stamford Bridge next term.
"I am waiting to see if the coach stays or leaves. If I stay, it will be because the team will be better than the season we have just had. I do not want to stay if we are less good," L'Equipe quotes Hazard as saying.
"Real Madrid can interest me, everyone knows it. But if tomorrow this club does not want me, we will not talk about it anymore. If they want to buy me, they know what to do.
"Go there for the sake of it... no. It takes a project. I still have a project in Chelsea. If I have a good World Cup, things will be easier."
Hazard is currently on international duty at the World Cup with Belgium, who will take on England, Panama and Tunisia in the group stage of the tournament.