Hazard has netted 10 goals in some influential displays so far this term to be the Blues' top goalscorer and his new-found work ethic has also delighted Mourinho.
"At the age of 23 to be where he is, we can only expect better," Mourinho said.
"But let him go. Let the top, top ones at 27, 28, 29 years be where they deserve to be because they have careers of many years at the top.
"And let Eden follow his way, the way he is doing.
"I cannot expect him to be the match-winner in every game; I cannot put this kind of pressure on him. But we are very happy with him. He has improved a lot in every aspect.
"He was known as one of the worst trainers. He was training to have some fun. Always having a joke. Not top concentration.
"He has become - I don't say one of the best - but a good professional in training.
"He works very hard for the team. He's trying now all the time to be an influence in our game. He's getting this responsibility."
Hazard, who was signed from Lille for £32m in June 2012, has been linked with a return to France with Paris St Germain but Mourinho insists he is not for sale.
"Between our tag of 'not to sell', plus the crazy amount that he can be valued at in this moment, I think there's no chance that Eden is going to leave," said Mourinho.