Hazard, who was Chelsea's top scorer with 14 league goals last season, has established himself as an talismanic playmaker since his arrival from French club Lille in 2012.
The 23-year-old has three years remaining on his current deal at Stamford Bridge, but the Chelsea boss said the club and player were keen to extend his stay.
"We have big hopes that he will go from a top player to reach higher levels," Mourinho told a news conference ahead of his team's opening Champions League group game at home to Schalke 04.
"He's a player we want to keep. It's true Chelsea is trying to have an agreement for a new contract. It will be a question of time. It will end with a new contract.
"He wants to commit to us and we want to commit to him for the future."
Hazard expressed his happiness at the club last week, explaining that new signings Diego Costa, who has scored seven goals in four games, and Spain midfielder Cesc Fabregas will help him play with greater freedom and less pressure.
Chelsea are top of the league having taken a maximum 12 points from their opening four games.
(Reporting by Sam Holden, editing by Ed Osmond)
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