Ratcliffe met with Amorim for crunch talks at the club's Carrington training HQ on Thursday.
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TalkSPORT says during the meeting, Ratcliffe told Amorim that "results must improve" and a top five finish is expected given the quality of the squad at the Portuguese's disposal.
European qualification is viewed as the "bare minimum" for United's board this season.
United meet Chelsea on Saturday night with Amorim insisting he won't be changing his maligned 3-4-3 system.