The team is currently in 14th place in the league and was recently eliminated from the Carabao Cup by Grimsby Town, a team from a lower division.
Amorim is facing a lot of pressure as the team has only earned 34 points in 33 league games and continues to use the same 3-4-3 system that has not been working well.
According to reports, United is preparing for the possibility of Amorim's departure and is considering giving Fletcher, 41, the task of managing the team temporarily.
Fletcher was hired as the Under-18s manager in June and has reportedly impressed the club's higher-ups.