The 39-year-old scored 41 goals in 142 appearances for the Gunners during a three-year spell which saw him lift the Premier League and FA Cup prior to a £25 million move to Barcelona.
And the Dutchman, who currently serves as Ajax's technical director, stated he would be open to returning to the English club, but ruled out going into management.
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“The way I work with Ajax, I do the transfers, the contracts and organise the scouting, so it suits me. It wouldn’t surprise me if I work in the future at Arsenal — it could be a possibility.
“I’ve never discussed it with Arsene Wenger. But if the board think about the future and make a list of people to work at the club, it wouldn’t surprise me if I am on the list of people. However, at this moment, I want to stay at Ajax.”
Wenger's men currently face a battle to qualify for next year's Champions League and, barring a miraculous second-leg comeback against Bayern Munich, are set for an eighth season without a trophy.
And Overmars cited the club's move from Highbury to the Emirates Stadium as a possible factor in their recent decline.
“I went back to Highbury to look around that area and still felt such a power there," he added. “When we were playing at home, we were unbeatable. That’s how we felt. But that’s the problem with a bigger stadium, often you lose that aura.
“It used to be intimidating at Highbury — that is the difference between the new stadium and the old one. When you build a new stadium, you must try to get the people as close as possible to the pitch.
“I was playing with Ajax in the old stadium and then the new stadium and we had the same problem. All the opponents wanted to play in this nice stadium so you lose that home advantage."