Having rediscovered his best form this season, Hazard has been strongly linked with a shock move away from the Premier League leaders.
Real Madrid have reportedly made the Belgium international their number one target for the upcoming transfer window, and are ready to table a world-record bid to tempt Chelsea into selling their star man.
But Desailly insists the 26-year-old’s inconsistency means he is not yet ready to take the next step in his career and move to the Bernabeu.
Speaking on the Alan Brazil Sports Breakfast, the former Chelsea and France defender was quoted saying: “It depends on his ambition.”
“I’m not sure Eden Hazard has that intention of being that top player, being first choice at Real Madrid.
“Remember, Hazard has been in the Chelsea system for five years, and he’s been doing well, but he’s not been doing what we expected of him – scoring goals and being the equivalent of Ronaldo or Messi, he’s not stable, he’s on and off.”
“I’m not sure he’s full ready to change and take the risk, because he will want to play regular football.
“The same thing goes to Atletico Madrid forward and Manchester United target Antoine Griezmann – is he really ready, does he have the desire to be in a competition for places at one of the top clubs and not playing football?”
While Desailly feels Hazard should stay, he (Desailly) acknowledges that Chelsea’s 18-goal top scorer Costa may take the opportunity to line his pockets in the Chinese Super League if the opportunity presents itself again.
He added: “He should go if he feels [like it].
“Money now in modern football is high and if a Chinese or another rich team comes for him in the summer, he will have to go.