Wenger is the Gunners' most successful manager, winning three Premier League titles and seven FA Cups in a 22-year career spanning between 1996 and 2018.
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But it was seven years before his appointment in 1996 that he started the long friendship with Dein.
Wenger was in charge of Ligue 1 side Monaco when he first visited Highbury for a north London derby on a flying visit.
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And Dein - who co-owned Arsenal from 1983 to 2007 and oversaw one of the club's most successful periods - has revealed it was his wife that led him to meet the Frenchman in 1989.
"When I joined the board the [directors' wives] were ushered into what they called the cocktail lounge, which was the overflow of the boardroom," Dein, who joined White and Jordan on talkSPORT to promote his book 'Calling the Shots: How to Win in Football and Life', said.
"And that's where Arsene was watching the game when he came over for that one game.
"And she made sure I went through to the cocktail lounge and met him, and suggested he come out for dinner with us."
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Wenger remained at Monaco for another five years before taking over at Japanese club Grampus Eight in 1995 and staying there for a year before Dein finally got his wish and appointed him as Arsenal manager.
And the former Gunners vice-chairman said he recognised Wenger's potential from the day he met him, given his unique background in medicine and economics, as well as being good with players, press and boards.
"I thought this guy… I had this vision at the time - Arsene for Arsenal," Dein said.
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"It's destiny. I'm not spiritual, but it was destiny. It's going to happen one day. Arsene for Arsenal, it's going to happen. But it took several years before it did, it took seven years before it actually came to pass."
He was unknown to many in the Premier League at the time, but quickly made his mark after eventually taking over from the sacked Bruce Rioch.
Less than two years after his appointment, Wenger became the first foreign manager to win the double, securing the Premier League title and the FA Cup in 1998.
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The rest is history.