"He knows how much it means to me and we will try to sort him out," said Wenger. "I'm convinced it means a lot to Robin to stay here.
"I've invested a lot of time in them (Van Persie and Theo Walcott) because I feel it is important to them and it means something to them to be at this club.
"He wants to be part of the club and, of course, we have to satisfy his demands as well. I don't think that we're far away."
Wenger's main concern is not trying to rely on the 25-year-old services too heavily.
"I believe him being fit has helped him greatly. He is a player who has made an extreme improvement," he continued.
"When you consider the player who arrived here, and who he is today, it's absolutely fantastic. He has ingredients which are very important - talent and motivation.
"The danger is to overplay him at the moment because we still have to be a bit cautious with him."