Real Madrid forward Cristiano Ronaldo landed the honour - awarded to the best player in world football - earlier this month, beating off competition from previous winner Lionel Messi of Barcelona and Bayern Munich's Franck Ribery.
Mourinho feels Hazard, who stated his own desire to become a Ballon d'Or winner earlier this week, could go on to reach a similar level.
"Now I say yes," said Mourinho. "Because his evolution is great.
"If he wants to be a great, great player and arrive where Cristiano and Messi arrives, he has the space to go - he's 23, and Cristiano is 28 or 29 (the Portuguese turns 29 next month), Messi 26 or 27 (26) ... still young players, but four or five years older than Eden.
"So he has the space to go, space for evolution. I think there's a great ambition for him."
Mourinho acknowledges that Ronaldo and Messi's prolific goalscoring records could make it difficult for a player such as Hazard to lift the Ballon d'Or.
"I think, because of the positions Cristiano and Messi play, they are also top goalscorers," explained the former Inter and Real coach.
"It's not just the quality of the players, but the number of goals they score that makes them even more special.
"Eden is a winger, a pure winger. Okay, we are giving him freedom to go to other areas, but he's an attacking winger.
"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 ... without injuries (then he has a chance). Messi and Ronaldo start and finish strong, players with big stability in their performances."
The lead-up to each Ballon d'Or announcement in recent years has been preceded by widespread debate over who deserves the award.
Mourinho added: "If he (Hazard) wants the Ballon d'Or, he must build the entourage politically for that.
"Without the entourage and the politics, he doesn't get the Ballon d'Or. It's a different story."
