It came close in the 2013-14 season but lost to Atletico Madrid in the semi-finals.
Chelsea failed to qualify for the Champions League in the last campaign and as they prepare to return to Europe's elite competition this season, the Belgium international is hopeful that his team can seal the trophy.
"Yeah, this year (to win it) is important... I have only got to the semi-final when we lost to Atletico Madrid. So it's in my head to win this trophy," the 26-year-old told British media.
"I have won the Premier League and the title in France. Now all the big players want to win the Champions League."
Hazard played his first game for Chelsea this season in Saturday's 2-1 league win over Leicester City, after recovering from an ankle injury sustained in June.
"It was a good test (against Leicester). I'm just happy to be back," Hazard added.
Following their Champions League encounter, Chelsea host London rivals Arsenal in the league on Sunday.
(Reporting by Aditi Prakash in Bengaluru; Editing by Raissa Kasolowsky)
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