Eden Hazard (Getty Images)
The Belgium international, currently on duty at the World Cup in Russia, has been linked with a move to Los Merengues for a long time and now appears open towards a move.
Hazard has stated that he will base his decision on whether or not Chelsea bring in top players in the off-season and whether or not manager Antonio Conte stays or leaves.
"I wait to see whether the (Chelsea) coach will stay or leave," Hazard, who has two years left on his contract, told L'Equipe.
"If I stay it's for the club to be better than last season. I don't want to stay for us to be poorer.
"Real Madrid could interest me, the world knows that. But if tomorrow this club does not want me any longer then we will not speak about it any longer.
"If they want to buy me they know what they need to do. I don't want to go there just for the sake of it. There needs to be a project.
"There is still a project at Chelsea. If I have a good World Cup, things will become easier."