Bakayoko reached the semi-finals with Monaco last term, but wants to do better with his new club and lift the trophy.
The France international, who joined for £40m in July, is set to make his Champions League debut for Chelsea against Qarabag on Tuesday.
When asked if he’d prefer to win the Premier League or European Cup this term, he said: “I would choose the Champions League because it is an exceptionally difficult competition. It’s not easy to win, so you should always grasp the chance to win it.
“For the Premier League, you always have the opportunity to win when you play for a club like Chelsea. So, if I have to choose between the two, it would be the Champions League.
“The Champions League has a different feeling to it, compared to other competitions. It is the number one competition in the world. It’s always been my dream to play in the Champions League and win it.”
Coach Antonio Conte has hinted he will make a number of changes to the starting XI, with top scorer Alvaro Morata set to drop to the bench in favour of Michy Batshuayi.
Bakayoko has played just two games for the Blues so far after recovering from a knee injury sustained at Monaco, but is hoping to be in the first team this evening.
Bakayoko and Rudiger model the new shirt
“I am really determined to start the competition with Chelsea,” he said. “Since I was young, I have had a good career and I gained a lot of experience last season.
“Chelsea is a great club, they always want to win trophies. So, it is certainly very important for me give my best for the club.
“The Champions League puts the pressure on us, especially when playing for a very big club like Chelsea. Chelsea want to win so we want that atmosphere and that pressure.”
The 2017-18 Chelsea FC third kit is available from today at nike.com/chelsea, and will be worn for the first time away to Atlético Madrid on September 27.