He now hopes Wenger will make the signings which could make his team a major force.
But looking back on recent seasons, Van Persie says the club should no longer be expected to win the title.
He told The Sun: "Every year it goes wrong in an identical way and that is frustrating. When you look at results in the last years, Arsenal shouldn't be talking about winning the League because too many times that has gone wrong.
"Of course the hunger and desire is great but sometimes you have to eat and be realistic.
"But I believe with the signing of a number of players, we should be in there competing for the prizes.
"Even now, it's still unbelievable we didn't win the Carling Cup as that was the breakthrough moment, showing everyone we could win a cup and create a belief within the team.
"When I talk about that it still hurts. It was so stupid and I ask myself 'how did that come about?'"