Chelsea endured a disappointing campaign last season, finishing a lowly 10th in the Premier League, meanwhile Leicester won the title, therefore securing Champions League football.
However, Kante has no doubts that he will eventually play Champions League football with his new club, despite not playing in the competition this campaign.
"Of course, I have never played in the Champions League. But everyone knows that Chelsea are a big club and I hope I will be playing in it next year," the France international said.
"Playing in the Champions League is a big dream of mine. When you are a player and have a chance to play in it, it's a good thing. But like I said, I hope to play in it next season.
"Chelsea is not a gamble. Because for me it's a new step. To stay in Leicester and play in the Champions League would have been a good step, but joining Chelsea is a good step too".