The 30-year-old collected a Premier League medal at Old Trafford last season, which was his first following eight years at Arsenal.
The Dutchman told MUTV: "I have three more years to go and I would like to stay longer.
"I want to play as long as possible at the highest level. Winning trophies is what it is all about."
Van Persie says his only disappointment from last season was not being able to find the back of the net during their Champions League defeat by Real Madrid.
The Spaniards won 3-2 on aggregate following the sending-off of Nani while the Reds were leading.
United open their European campaign on Tuesday against Bayer Leverkusen and Van Persie said: "It is probably my only regret about last year.
"The referee played an important part but I should have scored at least one or two goals in those games.
"I didn't, which I don't like. I have to improve on that. Hopefully we can do better this year."