By FOX Sports Staff
The Dutchman is currently assistant coach at Ajax under Frank de Boer and previously had a stint as the club's Under-19 manager. He retired from active football at the age of 37 after a successful 11-year spell with the Gunners in 2006.
Bergkamp is said to be of interest to the club hierarchy for the position and talks could develop in order to pave the way for the former striker's return to the north London club in May 2014.
The Gunners are in need of an able figure to replace Brady who achieved great success in the position and helped develop the likes of Cesc Fabregas, Ashley Cole, Wojciech Szczesny and Jack Wilshere. Brady announced his intention to step down at the end of the next season although the club are hopeful of retaining the Irishman's services as a consultant.
The former Dutch international could be interested in the role as he already specified a desire to return to Arsenal as recently as last month.
He told FATV: “We have started something good now at Ajax and I know a little bit in my role now, what I like and what I don’t like so if I could fulfil a similar role abroad, especially at Arsenal."
"That would be one of the things that I would like to achieve in the future. But not in the near future because we have just started here.”
Current manager Arsene Wenger has a contract till the end of next season and is expected to play a significant role in the efforts to persuade the former striker to take on the academy role.
Bergkamp scored 87 goals from 315 Premier League appearances during his time at Highbury and also had spells with Inter Milan and Ajax during his playing career.