Van Persie spent his first few years in north London as a talented but injury-prone winger before adapting his game to become the most feared striker in the Premier League.
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"I didn’t expect that he would be a striker, you know," Overmars, speaking to Absolute Radio's 'Rock 'N' Roll Football', said of Van Persie.
"I thought he would be a midfielder, but the boss, Wenger, was very good. At the time he bought excellent young players, and got Van Persie for £1.5m.
"When he came to Arsenal and got the chance to learn from Bergkamp, it was a great move for him. The transfer to Man United was not a big deal either. You have to give him credit.
"He played for Arsenal for six [eight] years. He performed and delivered and they got a great transfer, so everybody should be happy."