Having kicked off their campaign with a goalless draw against Wolverhampton Wanderers, who are involved in the UEFA Europa League playoff round, Leicester secured a 1-1 tie against a Chelsea side who will be playing in the Champions League this term.
"We want to break Europe," says Maddison, who set up Wilfred Ndidi's equaliser, in the video above.
"If you look at the quality throughout our squad, we've got the attacking prowess and the defensive structure to go and really push that top six.
"It's not an easy task - we should have won [at Chelsea] and we didn't - but it's one we'll be working towards, definitely."
Leicester's next test is a trip to Sheffield United, who are also unbeaten after their opening two matches, on Saturday.