The 43-year-old, who led the Seasiders to the Championship via the play-offs during his first full season in the hot seat, left his post on Thursday to be reunited with ex-England and Liverpool midfielder Steven Gerrard at Villa Park.
Critchley, who joined Liverpool's Academy in 2013, coaching the Under-18s and Under-23s, was unveiled as Aston Villa's assistant head coach after Michael Beale's appointment at QPR opened up a space in Gerrard's backroom team.
His departure came as a complete shock given Critchley — who celebrated his two-year anniversary in March — had said: "I'm in a very privileged position but I can assure you we want to keep improving. The ambition of the club is to improve on and off the pitch, so we want to move forward.
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"We're not content with where we are and I'm so pleased to be a part of it. It's been a really good two years and hopefully there are a few more years to come yet."
The centre back, currently in charge at Bolton Wanderers, made 230 league appearances for the Seasiders, initially on loan from QPR, and was promoted twice via the play-offs.
The second of those was in 2010 as Blackpool, under the stewardship of Ian Holloway, saw off Cardiff City in a five-goal thriller at Wembley to earn Premier League football for the first time in the club's history.
Michael Appleton, who owns the tag of Blackpool's shortest serving manager in their history, with just 11 games under his belt at the beginning of the 2012/13 campaign, is also an early contender, at odds of 10/1 with SkyBet and BetVictor at the time of going to print.
Others featuring in the market include: Dave Challinor (7/1), Karl Robinson (9/1), Michael Duff (10/1), Gareth Ainsworth (12/1), Leam Richardson (12/1), Jimmy Floyd Hasselbaink (14/1), Tony Mowbray (14/1) and Joey Barton (16/1).