Ablett, who had a season as Stockport manager in 2009-10, lost his 16-month fight against non-Hodgkin's lymphoma on Sunday night.
Former Liverpool manager Roy Evans told Sky Sports News: "It's a big shock. Obviously we know Gary's been ill for a while. It's a really sad day.
"He was good at everything he did as a player.
"He went into coaching and stamped his personality onto that and was doing a very good job, certainly at youth level. I remember he had bit of a difficult first spell at Stockport, but overall he's had a great career in football, he's a big loss to the sport.
"He made a big contribution to the game."
David Fairclough, who played for Liverpool between 1974 and 1983, added: "He was a lovely lad, he always conducted himself in the right way. He was great with people, always personable. What always came through with Gary was his attitude was just always very, very right."