Parry was loan manager at United, but has now departed, says the Daily Mail.
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For the moment, academy director Nick Cox has taken on the role, though a permanent replacement is being pursued.
Michael Appleton is again in the frame after previous reportes that he had turned down the role.
Appleton, a former United midfielder, has been in charge of Charlton and Blackpool over the past 12 months.
Parry had been with United since 2013.
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