The Magpies were hoping to lure Edwards to the post to replace Dan Ashworth.
The latter is on gardening leave as he chases a move to Manchester United.
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However, Fabrizio Romano states that Edwards is set to return to Liverpool in the summer.
He will take up a new role at Anfield, not one of sporting director, as he wanted a promotion.
Edwards left Liverpool a few years ago after working closely with boss Jurgen Klopp and owners FSG.