The Belgium international has been one of the star performers in the Premier League since moving to Stamford Bridge seven years ago, but gave a strong indication on Wednesday that his match-winning showing against Arsenal in the Europa League final would be his last appearance for the club.
Monaco midfielder Fabregas, who won two Premier League titles alongside Hazard, feels that he can go on and compete for both individual and team honours that have not been achievable in London.
"It is a difficult situation and a difficult opinion for me to have,” Fabregas told Goal.
"He has been at Chelsea – and I don't want people to think I am being critical of the club here – but I think it is time that Eden leaves and tries something else.
"I know he always says he doesn't care about the Ballon d'Or, but deep down it is something that I think every player feels would be a nice thing. I think I believe more than he does that he can win the Ballon d'Or, definitely. I know his ability. I know what he can do. I have played with the very best.
"I think at Chelsea, he could never win it. Not because Chelsea is not good enough or anything like that but there are teams and clubs that are so big with their image around the world that it makes a big difference. I think that at Real Madrid that Eden would win everything.
"He would kill it. He would be brilliant. I have no doubts. He is 28 - it is his last chance to have this. It is now or never. The other option is to stay at Chelsea, which could be a great move for him but only if he really wants it, is happy and he believes in the future of the team."