The Dutchman, who enjoyed a successful spell with the Gunners between 1997 and 2000, is currently a technical director at Ajax and believes that he could work in a similar role in North London.
Overmars told the Evening Standard: "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."
Overmars represented Holland 86 times during his career.