The former Gunners winger, who made 141 appearances and scored 40 goals for them between 1997 and 2000, has served as Ajax's director of football since the summer of 2012 but is poised to return to London.
Overmars, 44, is set to fulfil many of the duties performed by Dick Law, the club's transfer fixer who left at the end of last month.
Gunners boss Arsene Wenger has said in the past: "I never understand what it means, director of football. I'm manager of Arsenal and as long as I am manager, I will decide what happens on the technical front. That's it."