Hazard is currently under contract with the Blues until 2020, However, Real Madrid could renew their interest in the summer when the transfer window reopens.
Danny Murphy has issued concern in Real’s continued pursuit of Hazard, believing it could eventually leave Chelsea powerless to stop him leaving.
“If Eden Hazard stays fit and continues to improve, he can become one of the best five or six players in the world — and Chelsea must do all they can to keep hold of him,” Murphy told the Evening Standard.
“The last contract he signed was in February 2015, for five-and-a-half years, and worth about £200,000 per week.
“He is playing wonderfully well in a team who are within touching distance of regaining the Premier League title and he seems happy and settled on the pitch.
“But when the big clubs in Spain, particularly Real Madrid, want a player, they often get him.
“We know Madrid’s coach, Zinedine Zidane, is a confirmed admirer of Hazard.
“If Hazard becomes unsettled again — as he was for parts of last season under Jose Mourinho — I am sure Madrid would take him in a heartbeat because he is a truly fabulous talent.”