Van Persie struck both goals in victory at Norwich City on Saturday.
Wenger said: "My dream is that Robin stays until the end of his career. I will try to convince him."
Q: But why does he need convincing?
AW: "You need to convince every single player to extend their contract."
Q: Do you have to tell him about the ambition of the club, the money available for signings?
AW: "It is that as well, not only that, but that's the biggest part."