The 30-year-old striker, who joined the club from Arsenal at the beginning of last season, collected his first Premier League medal in May and hopes to add plenty more to his collection.
"I have three more years to go and I would like to stay longer," Van Persie told MUTV.
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Despite winning the domestic title, the Dutchman does harbour some regrets about last season, particularly in the Champions League.
Van Persie failed to find the net when United played Real Madrid in a 3-2 aggregate defeat to the Spanish outfit, with the Red Devils leading up until Nani's sending-off.
David Moyes's side host Bayer Leverkusen on Tuesday evening in their opening fixture of this season's Champions League campaign and the forward aims to make amends.
"It is probably my only regret about last year," Van Persie remarked of the Madrid defeat. "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."