Reports emerged over the weekend that Chelsea were eager to tie the Belgian, who joined from Lille in June 2012 for a reported fee of around £32 million, down on fresh terms.
And, speaking ahead of his team's UEFA Champions League opener against Schalke on Wednesday, Mourinho revealed discussions with the 23-year-old are under way.
"It's true that Chelsea is trying to have an agreement for a longer contract. He [Hazard] wants to stay for more years," said the Portuguese.
"We can feel every day his motivation improving - we have big hopes he can reach higher levels and become one of the best.
"He was always a kid living on his natural talent, which was amazing, but [he now has] tactical education [and] mental education.
"He can be one of the greats of his generation. Chelsea is the perfect environment for him to have that evolution."
In stark contrast to Chelsea's impressive accumulation of 12 points from their first four Premier League games of the season, Schalke have endured a tough start to their Bundesliga campaign.
Jens Keller's men have taken just one point from three matches, and were beaten 4-1 at Borussia Monchengladbach on Saturday.
However, Mourinho does not feel Schalke's domestic form will have any bearing on their Champions League hopes.
"I don't see that as a drama or as having a consequence in the Champions League," he added.
"Everything is different - probably the fact they lost their last match will make them stronger.
"They will have discussed their problems and will be a different team."
