The winger, 26, has won the Premier League twice, the EFL Cup and the Europa League during five years at Stamford Bridge, but is yet to taste success in Europe's elite club competition, fuelling his desire to go all the way.
After recovering from a broken ankle, Hazard made his first two appearances of the season for Belgium during the international break and is expected to make his Chelsea return against Leicester City at the King Power Stadium on Saturday.
The Blues then start their Champions League campaign at home to Qarabag on September 12, having not played in the tournament last season.
"We just want to win as many trophies as possible, for me personally I haven't won the Champions League so maybe that one would be a little bit more special," Hazard told The Daily Mail. "But I would prefer us to win everything.
"I think this year will be no different from the previous years, in the sense that every year it is difficult - especially when you play in many competitions.
"This year we have the Champions League as well and it is not easy to succeed in multiple competitions. But we will do our best and we have got depth in our squad so sometimes maybe one or two players can rest so they are 110 per cent for the next competition."
Hazard revealed he has a good relationship with manager Antonio Conte, but would not describe the Chelsea manager as a friend.
"You know on the bench, he has got a lot of energy moving along the sidelines and shouting instructions, but I think we need this personality in the squad to win football games," he said.
"I think we have got one of the best managers in the world, so we are really happy with him.
"I have a good relationship with all my managers. We train every day together and we can talk together and laugh together.
"Yes, absolutely we have a good relationship. I wouldn't say 'friends' because it is difficult to be friends with your manager so I wouldn't say that but we have a good relationship."
Hazard scored as a starter for Belgium in their 9-0 home win over Gibraltar, before coming on as a substitute in the 2-1 away victory in Greece as Roberto Martinez's men sealed World Cup qualification.
He netted 17 goals in all competitions for Chelsea last season, before his June injury, suffered on international duty, led to him missing all of pre-season and the start of the top-flight campaign.