It was reported on Monday that the Blues were keen to tie the Belgian international down to lucrative new terms at Stamford Bridge.
With the 23-year-old's current deal due to expire in 2017, Mourinho admits that he is hoping that Hazard will extend his stay in West London.
"It's true that Chelsea are trying to have an agreement for a longer contract," he told reporters. "We can feel every day his motivation improving. We have big hopes he can reach higher levels and become one of best."
Hazard joined Chelsea from Lille in 2012 for a fee thought to be in the region of £32m.