Brady has held the position since 1996, the same year that Arsène Wenger became manager, but has told the club of his intention to stand down in May 2014 when he will have spent 25 years at Arsenal as both player and coach.
Arsenal still want Brady to remain at the club in a consultancy role and he will also be involved in the search for his successor.
The early favourite for the position is Bergkamp, another legendary figure at Arsenal for his feats as a player at the north London club. Bergkamp has also made an impressive start to his own coaching career during five years at Ajax.
Having managed Ajax’s celebrated under-19 team, Bergkamp has risen to the role of assistant to manager Frank de Boer.
In an interview this month, Bergkamp outlined his desire to eventually work at Arsenal although he did also stress that he was keen not to leave Ajax prematurely. The timeframe, then, of potentially taking over from Brady in the summer of 2014 could be appealing.
Asked if he would consider a coaching job at Arsenal, Bergkamp said: “I would, yes.”
He added: “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 fulfill 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.”
Arsenal will not rush their search for Brady’s successor, with the position regarded among the most important at the club.
There is, however, an appreciation that it could be advantageous to have the position taken by an iconic former player, such as Bergkamp, particularly when it comes to the highly competitive job of persuading the best young players to join your club.
The forthcoming departure of Brady follows the loss of Pat Rice, Wenger’s assistant, last year. Both had been at Arsenal throughout Wenger’s tenure, with the Frenchman’s own contract due to expire in 2014.
With Premier League clubs now introducing the new Elite Player Performance Plan, it is understood that Brady regarded next year as a logical time to depart.
Brady joined Arsenal as a 15-year-old youth team player in 1971 before making his senior debut two years later. He was part of the 1979 FA Cup-winning team.
After managing at Celtic and Brighton, Brady returned to Arsenal under Wenger where he has helped develop Ashley Cole, Jack Wilshere, Cesc Fabregas and Kieran Gibbs.
Arsenal have also won three FA Youth Cup titles since 1996 as well as back-to-back academy Premier League titles in 2009 and 2010.
“Liam has a deep understanding of what it takes to discover and develop a talented youngster into someone who can perform at the highest level,” said Ivan Gazidis, the Arsenal chief executive.
“He has made a massive contribution to Arsenal Football Club. It will be difficult to find a worthy successor but we will be looking for someone who can build on what Liam and his team have created,” Gazidis added.