The Belgium international revealed this week he had made a decision on his future and would announce it "soon".
Hazard, 28, has long been linked with a move to Madrid but is contracted at Stamford Bridge until 2020.
His former team-mate Fabregas, who moved to Monaco in January, is holding out hope Hazard will stay at Chelsea.
"Let's see what he decides to do. He has a year and a half left and he is happy at Chelsea and so is his family," Fabregas told Radio Marca.
"But in the end they are very personal decisions. He likes Madrid and he has always said it.
"Hopefully he will renew with Chelsea, but if he does not he will finish in Madrid."
Goal understands Hazard is hopeful of securing a £100m move to the Los Blancos in the summer with Isco potentially the man to make way.
The Belgian was sad to see Fabregas leave Stamford Bridge last month, declaring he was lucky to have played alongside the Spaniard.
"In five years I can say that I was lucky to play with him," Hazard said.
"Since the beginning when he came, we saw it the first year, we won the double together.
"Top guy on the pitch, off the pitch, a great friend of mine. I hope he will have a good future."