The 29-year-old Holland striker says the fact United have a track record in valuing older players such as Ryan Giggs and Paul Scholes may persuade him to see out his playing days at Old Trafford too.
Van Persie told Dutch magazine Voetbal International: "For the next few years I will be at Manchester United - and maybe longer. United could be my last club."
The former Arsenal striker's current United contract will end when he is 33 but with 39-year-old Giggs and Scholes, 38, for inspiration, the striker may be tempted to extend his time at the club.
"You have a number of clubs in Europe where older players can find it good, where they are valued. You used to have that at Juventus and AC Milan, Manchester United today is a good example. So who knows how long I will stay at the club," he added.
"There is a new challenge for me every day at United. My development is an ongoing process. That gets an extra boost when you are surrounded by new coaches and team-mates, all with their own ideas, in a totally new environment."
Van Persie scored twice for Holland against Romania last night to overtake Johan Cruyff's international goal tally. Cruyff scored 33 goals in 48 appearances of a curtailed international career and van Persie is now on 34 goals from 74 caps.
Van Persie is second in the Premier League scoring charts this season with 19 goals, three behind Liverpool's Luis Suarez, and United will be hoping his international form will see him pick up domestically after a spell of just one goal in 10 matches for the club.