Ablett lost his 16-month battle against non-Hodgkin's lymphoma on Sunday.
Former team-mates have spoken of their sadness at his death with Paul Walsh, who played alongside Ablett at Liverpool in the 1980s, describing the news as "absolutely tragic".
"I'm absolutely stunned at the news. He was a hell of a nice person. He was a top lad," he told Sky Sports News.
"He didn't do anything fancy but was a great pro who trained hard with a great attitude to everything he did.
"There was also a steely determination about Gary. You don't get in the Liverpool team and come through the ranks at Liverpool and play 100 times for them if you haven't got that little bit of steel."
Ablett, the only player to win the FA Cup with both Merseyside clubs, also went on to play for Birmingham, Wycombe, Blackpool and the American side Long Island Rough Riders before turning to coaching.
He spent some time with Everton's youth set-up before replacing Paco Herrera as the coach of Liverpool reserves, where he won both the Premier Reserve League North and also the national title in 2008.
Ablett left Liverpool a year later and was appointed Stockport manager at a difficult time for the club - they were in administration - and left after a season following a change of ownership.
Former Liverpool and Germany midfielder Dietmar Hamann, who became Stockport manager in 2011 a year after Ablett left the post, said: "It's devastating news. He's a very highly regarded and respected man on Merseyside and a true legend."
Michael Owen said on his Twitter account: "So sad to hear the news that Gary Ablett has passed away today aged 46.
"He played for some great clubs and had a career to be proud of. RIP."
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Top man and decent no frills footballer. R.I.P. gary and condolences too all family and friends. UTID !!!!
Terrible, terrible news. Gary conducted himself with great dignity and grace despite having a very difficult time at County. He was a real gentleman, a true professional and a great role model for younger players. Thoughts are with his family.
Don't think he was ready to manage when he came to County, it's much more than coaching which he at least had some experience of. Certainly should never have been appointed manager of a club in County's position but of course that didn't make him a bad person and nobody deserves their life cutting short at what is barely middle aged. RIP Gary
Terribly sad news - Gary was a real gentleman. Best wishes to Gary's family.