The Blues forward has enjoyed a fine season and has set his sights on rivaling the pair for major individual prizes but accepts their stats will be hard to equal.
The Blues' top goalscorer this season has been in blistering form in 2013-14, notching 11 times in 34 matches as he continues to flourish under Jose Mourinho, but accepts that reaching the top level will prove no easy feat.
"I realize that I can compete with Messi and Ronaldo in the near future, if I put in some more effort," he told Het Laatste Nieuws.
"Previously I was more worried about the game itself: Football was just a game for me - I wanted to amuse myself and didn't bother what the people thought about me - but since I've been here at Chelsea I've become more aware of my qualities, I guess. Before, I knew I was a good player but not one of the better players in the world."
"I've matured," Hazard continued. "On the pitch I haven't changed much, I'm still the same, but I realized that, if I want to be among the best in the world, I'll have to perform consistently, game in, game out.
"I'm now important for the team, I give good passes, I score more goals and Chelsea are performing well. Everyone expects more from me. I hear it every day. Maybe I need these little comments, too."