Ablett made his debut in 1986 and played 109 games for the Reds, scoring once, until he left for Everton in 1992.
He returned to Liverpool in 2006 to take up the reserve team coach position when Paco Herrera left the club.
In April 2008 he guided them to the Premier Reserve League North title, and the following month they became national champions, before leaving the following season.
A statement from the League Managers Association said: "Respected throughout the game by players, coaches and managers alike Gary will be sadly missed. The LMA’s thoughts and condolences are with Gary’s wife Jacqueline and children."