Chelsea chairman Bruce Buck insists the club will do all they can to get Hazard - who has seven Premier League goals to his name already this season - to stay at Stamford Bridge.
Buck spoke at the 'Financial Times Future of Football' event in Doha, remarking: "Every Chelsea fan in London and around the world loves Eden Hazard, and he's not only a great footballer but I think he's a wonderful lad.
"We want him to stay and we will do what we have to do to entice him to stay."
The 27-year-old's situation has been monitored for a while by 'Los Blancos', who are looking for a big-name replacement for Cristiano Ronaldo, who departed Real for Juventus in the summer.
In the meantime, Hazard and Chelsea take on Manchester United in the Premier League on Saturday.