Fletcher, 18, is the son of United coach and former captain Darren Fletcher.
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With United pushing to agree terms with Brighton for midfielder Carlos Baleba, Amorim has given Fletcher call-up this week.
Fletcher is yet to make his senior debut for United, though made the matchday squad seven times last season.
He and twin brother Tyler are regulars with the U18 and U21 teams at United after leaving Manchester City almost two years ago.
United host Arsenal on Sunday to kickoff their Premier League season.