Hazard has twice been named Chelsea's Player of the Year since signing from Lille in 2012, winning the Premier League, EFL Cup and the Europa League during his time at Stamford Bridge.
He endured a torrid campaign in 2015-16, scoring just six goals in 43 appearances in all competitions.
But Cole, who played alongside Hazard when spending the 2011-12 season on loan at Lille, believes the Belgium international is destined to be revered at the club for years to come.
"I think he'll go down as Chelsea's greatest player," Cole told CFC Fan TV.
"He's certainly the most talented all-round footballer I've played with and he's already a hero with the fans. I hope he stays there for the rest of his career.
"My first game in France with Lille, [then-coach] Rudi Garcia was saying to me, 'we've got this good kid, Eden Hazard'.
"He said 'I want you to play with him'. And then he scored two of the best goals you'll see within 20 minutes and I thought, 'I don't know if I'm good enough to play with him'.
"He's just a nice kind, he's got a good way about him, he loves training, he loves football and everyone in that dressing room in France loved him."
Chelsea sit eight points clear at the top of the Premier League and Cole - who considers Tottenham as the Blues' most threatening title rivals - has been impressed by the impact of Antonio Conte.
"Already his team has got his personality. They look strong. You can't see anything else than Chelsea winning the league now," said Cole.
"The only thing that would make me a little bit nervous is if Costa picks up a long-term injury. And the other thing is that Tottenham look like a good team this year, which is bad news.
"Harry Kane and Dele Alli would get into most teams around the world. But apart from that, I think Chelsea are still a good couple of gears ahead of them.
"You've got to give him credit, he's come over to a new country and his language is good, but it must be so hard because he's such an expressive man."I imagine most of his management skills are his emotional connection and how he speaks to people and to go to another country and do that shows how exceptional he is."