The Netherlands striker has netted 19 Premier League goals since joining from Arsenal in August, inspiring United to the brink of a 20th top-flight title.
"For the next few years I will be at Man United - maybe longer," the 29-year-old was quoted as saying by the BBC on Wednesday. "United could be my last club."
Van Persie has been enthused by the new challenge after eight years at Arsenal where he only won the 2005 FA Cup.
United manager Sir Alex Ferguson's attitude towards older players, with 39-year-old Ryan Giggs and 38-year-old Paul Scholes still on the books, has also led the Dutchman to ponder whether he is better off staying for good.
"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 said.
"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."
Ferguson himself is part of that refreshing change, with Van Persie seeing a fun side to the 71-year-old.
"He is one of the friendliest people I have ever come across in my life. Of course Ferguson has another side, when he is in the game mode. Then he is a warrior just like us, the players on the field," he added.
"Netherlands coach Louis van Gaal is the same. People base their opinions on what they see on TV of him. That is 20 percent of the reality. I get it, it is human to judge that way, but for good judgment you need more information."
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