The Belgium international has been linked with a switch to the Santiago Bernabeu for several years, with his performances at Stamford Bridge lifting him into a talent bracket alongside the global elite.
No deal has been done as yet, but Hazard has remained evasive of late when it comes to the question of his future in England and possible fresh terms in west London.
Sinclair believes the 27-year-old could soon be on the move, allowing him to test himself at the very highest level, with it likely that Madrid will seek to test Chelsea’s resolve if they choose to part with Gareth Bale.
"Chelsea will be doing everything they can to keep him there for at least another year, but Real Madrid were linked heavily last year and could come back in for him again.
"With Bale potentially leaving Madrid, I think Real will have a list of players that they will want to replace him with, and I believe that Hazard will be on there.
"Hazard is a crowd-pleaser and definitely a big-name player that Madrid like to bring in.
"I think if you put him on that stage and at a club like Real Madrid, he’ll improve and become a better player."
Sinclair is the not the first former Blue to warn those at Stamford Bridge that they risk losing a prized asset in the next transfer window, with Eidur Gudjohnsen having also expressed concern regarding Hazard’s future.
He told Omnisport when quizzed on whether the Belgian will be staying put: "I hope so.
"I'm afraid maybe not, but from what I understand he seems very happy.
"He wants to know where Chelsea are going, what direction, which coach is coming, whether [Antonio] Conte is staying or someone else.
"A lot will depend on how Chelsea present the future to him to convince him that he should be there for a long time."