Kuyt believes the Reds can push on under new boss Kenny Dalglish and owners Fenway Sports Group.
He said: "I signed up (to a new contract) because I have faith in the club.
"Everything I noticed shows the ambitions are high. The appointment of Steve Clarke, assistant to (Jose) Mourinho at Chelsea, is one example. Just a very good on-the-pitch coach. That sort of thing.
"The club strives again to get to a level that suits the club.
"I feel that I am at one of the top clubs in Europe. The goal is still to become champions and win cups, and I will help."