Blancos boss Zinedine Zidane has reportedly identified Hazard as his number one transfer target this summer, labelling him as a "fantastic player" ahead of a major squad overhaul.
The Belgium international has enjoyed his most prolific season yet at Stamford Bridge, scoring 16 goals in 33 Premier League appearances, which has only increased his market value.
Melchiot, who played for Chelsea between 1999 and 2004, has urged his old club to cash in on Hazard while they still can, with his existing contract set to expire in 2020.
“Keeping him for another year and letting him go for free? That would be bad business," he told talkSPORT on Monday.
“As a fan, all along I want to keep Hazard until the last minute. But as a business, it would not be a smart move to hold onto him.
“You don’t want to let anybody walk out for free.
“If you can get a lot of money for him… he’s on his last year and still has a value of around £100m. If they can get that for him, it would be great.”
The Blues are facing a two-window transfer ban for breaking rules regarding signing minors from foreign clubs, which means as it stands they may not be able to bring in a replacement for Hazard until next year.
The mercurial attacker has been one of the few bright sparks for Maurizio Sarri's side during a frustrating season which has seen them slip out of contention for major trophies.
A 2-0 defeat away at Liverpool on Sunday severely dented their hopes of a top-four Premier League finish and winning the Europa League might now be their most viable route to Champions League qualification.
Melchiot went on to admit that he understands why Hazard would want to make the step up to Madrid, with his insatiable drive to be the best likely to see him seal a move sooner rather than later.
“Hazard’s future at the club is very simple,” he added. "This kid wants to play the best and wants to play with the best.
“It’s great being the best player in a team, but you want to make sure you’re playing amongst players who can help you succeed and bring you to the next level.
“I’m not saying the current Chelsea players are not good… but are they good enough to keep him excited?
“That’s why Real Madrid is so interesting for him and that’s why he might have already made his mind up.”