The Belgium international has been a key figure in Chelsea’s title pursuit this season, scoring nine goals in 22 Premier League games.
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"Does he have the capacity to reach the level of a Messi or Cristiano? Now I say yes, because his evolution is great,” Mourinho told reporters.
“He has time to become a great, great player and arrive where they are – he's 23, and Cristiano is 28, Messi 26 – so there is space for further evolution, and there's a great ambition in him.
“They are also top goalscorers, of course, and that makes them even more special. Eden is a winger, a pure winger, so I don't think it's possible for Eden to be top scorer in the league. That normally affects people's judgement.
"But if he can be a match-winner, a player with high performances during a season, what I feel now in him is responsibility in every aspect.
“Against Manchester United he made a fantastic tackle in our own box.
“Against Stoke, he tried to kill the game, have initiative, dribbling at people, trying to make things happen. The kid is going in a fantastic direction."
But despite his praise, the Chelsea manager warns that Hazard may have to do more off the pitch in order to stand a realistic chance of winning the Ballon d’Or.
"If he wants the Ballon d'Or, he must build the entourage politically for that," Mourinho said.
"Without the entourage and the politics, he doesn't get the Ballon d'Or. That's a different story."