Amorim will officially take over as the new United head coach on November 11 after he serves out his notice period at Sporting.
Van Nistelrooy will manage United in their fourth Europa League match against PAOK on Thursday and for the visit of Leicester City in the Premier League on Sunday.
United could introduce Amorim at the start of the November internationals and the 39-year-old is expected to be joined by up to five backroom staff members from Sporting.
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