Ablett, 43, left his post as Liverpool's reserve team manager in May and is believed to have beaten off competition from former Celtic and Northern Ireland midfielder Neil Lennon to land the post.
Jim Melrose is heading a consortium which is on the brink of completing a takeover which will bring the Edgeley Park club out of administration.
Raynes said: "I've just been in a meeting with the new gaffer and everything he said was really positive.
"He's played with, in his own words, some of the best players that Britain has ever seen during his playing career with Liverpool.
"It's a great appointment and hopefully the club can now kick on and start moving forward again once the takeover has been completed."