Overmars follows Monchi, who recently left Roma to rejoin Sevilla, in rejecting the possibility of moving to the Emirates.
Arsenal are searching for a replacement for Sven Mislintat, who left the club earlier this year.
But will now have to look elsewhere with Overmars insisting he is still motivated by the challenges at the Dutch giants, who have reached the quarter-finals of the Champions League this season after knocking out three-time defending champions Real Madrid.
“There are still plenty of challenges at Ajax and I’m having a good time here,” Overmars said.
“We are taking steps with both the youth academy and the first team. From a sporting point of view, we still want to show a lot.
“What is also important to me , is that it is nice to work with the people around me. I get pleasure and satisfaction from that.”
The 45-year-old spent three years in north London and was part of Arsene Wenger’s double-winning side in 1998.
Since becoming the director of football at Ajax in 2012, after a spell as a youth coach at the club, the former Barcelona star has helped to spark prosperity despite a willingness to sell their best players.
This season’s side has enjoyed success after precocious talents, such as Frenkie De Jong and Matthijs De Ligt, have been blended with experienced operators such as Dusan Tadic and Daley Blind.