I think RVP said recently that no amount of money will sway him, he needs to see that we are serious about contending for honours, he obviously wants us to sign some more players. One thing I will say though is that no matter how talented he is, he's just one player, he's not bigger than the club and it seems that whenever our best man leaves we are the ones earmarked for 5th/6th/relegation/whatever.
We've seen a lot of top players leave over the past decade, we've always been singled out by other fans and by the media, saying we won't be able to keep our Champions League spot or we won't be able to compete but we always do. Some of the short sighted Arsenal fans forget that only a few seasons ago we had a team which could and should have won the league. There'll always be new players to replace the outgoing ones and we'll be fine.
We can't go around signing every big name player just because one of our current players wants us to, no matter how talented van Persie is he does have a shady injury record. If he wants a good Bosman deal then he's going to play out of his skin for the upcoming season and that is only going to benefit Arsenal. Yes, we could sell him and get a decent amount, but we aren't exactly a poor club, we need to buy players that will strengthen the areas that need strengthening, not buy players just to pander to one of our current ones.
Another thing which people will point out is the amount of goals he scored for us last season and the percentage of the teams goals which came from him, but look at Real or Barca, if you take Messi or Ronaldo out of those teams that's a huge chunk of goals missing, the same could be said for pretty much any other team who relies on a striker to score for them. It doesn't mean we won't be able to find players who will contribute, we might not be able to get another 30 goal a season striker, in fact it's damn near impossible to just go out and buy one unless you're Man City, but if van Persie leaves next summer it won't be the end of the world.