Ibrahimovic was one of Europe's most highly-rated teenage players when he met Wenger in 2000 to discuss a possible move to the Premier League club.
But Wenger was keen to check out Ibrahimovic during a trial first and the Swede was unhappy at what he perceived to be a lack of respect for his talents.
Ibrahimovic told The Sun: "Arsene gave me the famous red and white jersey - the number nine shirt with Ibrahimovic on it and I was so pleased I even posed for a picture wearing it.
"It was a fantastic moment for me. Arsenal had a great team then and here was an Arsenal shirt made just for me.
"So then I waited for him to convince me that I should join Arsenal. But he didn't even try.
"He never actually made me a serious offer, it was more, 'I want to see how good you are, what kind of player you are. Have a trial'.
"I couldn't believe it. I was like, 'No way, Zlatan doesn't do auditions'.
"I thought 'You either know me or you don't and if you don't know me you can't really want me'."
Ibrahimovic instead chose to join Dutch club Ajax before spells at Juventus, Inter Milan and Barcelona.
The 30-year-old starred as Milan took a 4-0 lead in their Champions League tie against Arsenal last month and he has another chance to show Wenger what he missed out on when the Italian club travel to the Emirates Stadium for the second leg on Tuesday.
"I definitely made the right choice," he added.
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