Kuyt's agent Rob Jansen was quoted on Monday as saying his client was considering his future after interest from Inter, but the Holland international is adamant he will respect the contract extension he signed in April.
He told Voetbal International: "As far as I know there is nothing true about this. I am very happy at Liverpool.
"I didn't extend my contract for two years three months ago for nothing. You don't do that if you have the intention to go away quickly."
Kuyt, 31, was a substitute for the opening-day draw with Sunderland but started Saturday's win at Arsenal before making way for Raul Meireles after 71 minutes.
And the former Feyenoord man accepts Kenny Dalglish's summer spending spree means he may just be a squad player this term.
He added: "Maybe people think that I want to leave. But it doesn't work like that for me.
"Liverpool has a very big squad and therefore you could sometimes be on the bench.
"It's my intention to stay here, though you know nothing is certain. In football things can be different tomorrow."