Speculation continues to suggest that the Belgium international is destined to make a switch to the Santiago Bernabeu at some stage.
He is approaching the final year of his contract at Stamford Bridge and has offered no indication that he will be penning fresh terms despite vowing to make a decision on his future “soon”.
Chelsea are about to enter a two-window transfer embargo, which would prevent them from moving to bolster their ranks, but they do have a £58 million ($73m) deal in place for United States international Christian Pulisic.
His summer arrival would help to soften the blow of losing Hazard, with former Blues defender Melchiot considering it to be a matter of time before the 28-year-old goes searching for silverware outside of west London.
He told the Daily Star: “Some of the questions that Eden Hazard will ask himself are: ‘Can I win trophies here? Can I become a better player than I am already? And in this team can I move forward as quick as I want to move forward?’
“And if all those answers are no, what do you think he’s going do? I don’t see him staying at Chelsea.
“They have to sit down with him as quick as they can because if not the kid has all the power in his hands, he’s going to run the contract out and it doesn’t matter what they do.
“They can do whatever they want, they can tell him ‘you have to sign now’ or whatever pressure they want to put on him, they’re already too late.
“So they might as well now have the conversation and be open about it, say ‘look, I know you understand we extend your deal and we give you whatever it is that we can give you, or we’ve got to let you go. Because if not we’re not going to make any money on you’.”
Hazard started on the bench in Chelsea’s most recent Premier League outing, with Maurizio Sarri favouring other options before turning to the Belgian in a dramatic 2-1 victory over Cardiff.