Fabregas was tearful as he applauded all sides of Stamford Bridge following Saturday's 2-0 FA Cup third-round win over Nottingham Forest, during which he had a first-half penalty saved.
The 31-year-old's contract expires this summer and he has been linked with a January move to Monaco, and a reunion with former Arsenal team-mate Thierry Henry.
Fabregas joined Chelsea from Barcelona in June 2014 - two years after Hazard arrived from Lille - and has won two Premier League titles, plus the 2015 League Cup and 2018 FA Cup, during his spell at Stamford Bridge.
"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.
"Just admiration about this guy. I hope he will have a good future. It's a bit hard now, but he's still very good and he will enjoy."
Any move is still to be completed, but Fabregas' emotional reaction after his 501st appearance in English football suggested it was goodbye.
Another player who has been linked with a move is Callum Hudson-Odoi, who set up both goals for Alvaro Morata against Forest.
The 18-year-old winger, whose contract expires in June 2020, is reportedly a target for Bayern Munich.
Hudson-Odoi is eager for further opportunities and knows he could be given them due to Chelsea's injury situation.
Striker Olivier Giroud (ankle) and winger Pedro (hamstring) could come back into contention for Tuesday's Carabao Cup semi-final first leg with Tottenham.
But Ruben Loftus-Cheek appeared to aggravate a back injury against Forest in a game Willian missed with a hamstring problem sustained against Southampton last Wednesday.
Hudson-Odoi told Chelsea TV: "I've just got to be patient and keep working hard, no matter what. I've got to keep pushing in training.
"The injuries are unfortunate. For me I've got to keep working hard and hopefully my chances will come."