Van Persie hit the winner against Everton on Saturday - just a day after the Club unveiled statues of Herbert Chapman, Tony Adams and Thierry Henry, the latter of whom is currently training with the squad at London Colney.
Walcott told arsenal.com: "The way Robin is playing, he wants to be one of those legends as well. I'm just absolutely shocked. To see that go in was incredible.
"He's a player in so much form, the goal was amazing and it's just world class to see.
"He would say himself, he was in and out of the game. That's the difference. Give him any chance and he scores when he wants, as the fans say!"