The former Gunners winger has been linked with a return in that role.
And that would see some of Arsene Wenger's responsibilities delegated to the Dutchman, such as targeting players in the transfer market.
Overmars became a much-loved figure at Arsenal among fans during his three-year spell at Highbury.
And it appears he is set to be back in north London after this season.
According to TuttoMercatoWeb, Overmars will leave his position at Ajax at the end of the current campaign.
It is claimed he has reached an agreement with Arsenal to begin work from next summer.
While it is not specified exactly what role Overmars will undertake, it is expected to be in the form of a sporting director.
Arsenal do not currently have a sporting director at the club.
But with Wenger's deal expiring in 2019, there are set to be changes behind the scenes at the Emirates.
Overmars has impressed at Ajax with TuttoMercatoWeb adding all has been decided and he will say goodbye to the Eredivisie side.
The 44-year-old has been sporting director at Ajax since 2012.
Since then, the club has won two league titles and reached the Europa League final last season before losing to Manchester United.
