Hazard has been strongly linked with Real for several months after the Belgium star refused to rule out a move to the Bernabeu and admitted playing for the Spanish giants would be a dream come true.
The 27-year-old’s current contract with Chelsea expires in June 2020 and he is yet to agree to an extension as he weighs up his future.
Chelsea have reportedly offered to make Hazard the highest paid player in the club’s history in a bid to keep him.
But, ahead of Saturday’s Premier League clash against Leicester, Zola made a persuasive argument that was aimed to appeal to Hazard’s ego rather than his bank balance.
Zola was voted the best player in Chelsea’s history in 2003 after serving the club with distinction as a gifted playmaker with similar skills to Hazard.
The Italian, now back at Chelsea working for boss Maurizio Sarri, believes Hazard is capable of stealing that cherished title from him if he stays at Stamford Bridge.
“He’s certainly one of the players who has given this club a lot of satisfaction,” Zola said.
“He is 27, and hopefully he will stay long with us and become even bigger.”
Since arriving from Lille in 2012, Hazard has already established himself as a Chelsea great, playing key roles in two Premier League title triumphs, scoring the winning goal in last season’s FA Cup final and also lifting the Europa League and League Cup.
– Back to his best –
After an inconsistent campaign last term marred by rumours of a rift with then manager Antonio Conte, the midfielder is back to his best this season, scoring 10 times in all competitions so far.
Hazard underlined his enduring value to Chelsea when he shrugged off a back injury to clinch their 1-0 win over Bournemouth in the League Cup quarter-finals on Wednesday.
Hazard was not risked from the start due to a foot injury, but came on to score the decisive goal and is expected to feature when fourth-placed Chelsea host the Foxes this weekend.
“The difference was the changes we made. When Pedro and Eden came on, they gave us an extra gear,” Zola said.
“Eden is the type of player who can make a big difference when he comes on, even for 20 minutes.”
Jamie Vardy is set to return for Leicester after he was rested for the League Cup defeat against Manchester City on Tuesday.
Vardy has been struggling with a groin injury and Leicester boss Claude Puel did not want to risk aggravating the problem in midweek.
But Leicester’s five-goal top-scorer should be available to face Chelsea as he tries to kick-start his spluttering season.
“I hope Vardy can be fit for this match and can find his qualities,” said Puel, whose mid-table team have gone four games without a win in all competitions.
“With his quality and his aggressiveness, he is a very good player for us. We need Jamie, with his ability, capacity and character, to give his best.
“Of course, it has been difficult for him with injuries and suspensions this season, but he is a valuable player for us and we need Jamie to be at his best for us.”
Ben Chilwell could also start after the England left-back missed Leicester’s last two matches with a knee injury.