The Dutchman boasts an astonishing record of 33 goals in 32 matches for the Gunners in 2011, including an exquisite volley which earned his side victory over Everton on Saturday.
Walcott admits he was blown away by the goal, and believes Van Persie can acquire legendary status at the Emirates Stadium if he maintains his blistering form.
"Any little sniff and he just grabs it,” he told reporters. "That's one of the best goals I've seen for a long time.
"It was a moment of magic from Robin. He's done that so many times before and yet it was an absolutely fantastic goal.
"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!”
Statues of former greats Herbert Chapman, Tony Adams and Thierry Henry were unveiled outside the Emirates Stadium as Arsenal celebrated their 125th anniversary in style.
"It's an absolute honour to be part of it, to see the number of legends taking part in the day made it very daunting,” Walcott added.
“There were a lot of world-class players on the field.”
Henry, now with the New York Red Bulls, has been training with the Gunners squad at London Colney during the MLS off-season, and Walcott believes the Frenchman is still a force to be reckoned with.
He continued: "Thierry still looks good, [he] is training with us and you hear the fans chanting 'sign him up, sign up.' I don't know if there's any chance - you'd have to ask the boss that.
"He's still fit, playing in the MLS and enjoys playing his football so much that I don't think he wants the break.”
Walcott also revealed the occasion spurred him and his team-mates on to get the win, although he admitted it also ramped up the pressure.
"Everyone was really up for it,” he said.
“We had a job to do, we couldn't be too into it and we tried to forget about it a little bit on the pitch.
"If we didn't get the right result then it would have been a very disappointing day.”
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