The 31-year-old striker, who began his professional career at Feyenoord, made his debut at the age of 17 for the Rotterdam club during the 2001-02 season.
Van Persie told the Manchester Evening News: "I want to go on as long as possible.
"I want to go to the World Cup when I am 35, and I want to play professional football until I am 40. Most probably, it will be for a less famous club by then, but I do want to play as long as I can.
"Every target I have set myself up until today in my career I have reached. So I am going to get the other targets, too."
Van Persie has won an array of trophies and accolades during his career, including the FA Cup with Arsenal and the Premier League with his current club.