Mourinho did not wish to compare the 23-year-old Belgian with "monsters" Cristiano Ronaldo and Lionel Messi, but recently suggested Hazard needed to add goals to his game in order to be considered in the same category.
And Hazard struck a hat-trick in Saturday's 3-0 defeat of Newcastle which saw Chelsea go top of the Premier League.
The goals took Hazard's season's tally to 14, including 12 in the top-flight, and he has impressed even when not scoring, including in last Monday's crucial win at Manchester City.
"He is special," Mourinho said.
"I don't want to compare him with the monsters, because the monsters have 10 years of career, winning trophies, scoring goals; I think it's not fair for the monsters and it's not fair for the kid to make that comparison.
"But I don't see a better young player. I think in this moment he's the best young player in the world.
"Maybe with the hat-trick he has the chance to win, one day, the (Premier League) player of the month (award), because he never gets that.
"He's not good enough for that? Because other players are better than him? I don't know. I'm just saying.
"I like other guys to win, I'm happy for them. But I would like my guy to win it once."
Hazard was disciplined by Mourinho earlier this season after missing the Champions League home clash with Schalke.
A lost passport delayed his return from France, where he was watching his former club Lille in action, and saw him miss a training session.
Mourinho added: "When he went to Lille, he went because he was invited by the club and he didn't think about the possibility of being late and missing a training session. It was a naive thing.
"Immediately he reacted well. This was an isolated episode, because the reality is that since the pre-season when he understood the levels of professionalism I demand from my players day by day.
"He's just working well and hard to try to be as good as possible."
Hazard's work ethic has impressed Mourinho, who was scathing of his players following the 2-0 loss at Newcastle on November 2.
Chelsea have lost just once since and are unbeaten in 10 games entering Tuesday's match at West Brom.
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