Defeat at Brentford has United sitting in 14th place on the Premier League table, with no European football this season and already out of the Carabao Cup.
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The situation has turned up the heat on Amorim amid reports United's board have drawn up a shortlist of names to potentially replace the Portuguese.
The Daily Mail says United will need to pay over £12m to axe Amorim.
Amorim was appointed on November 1 last year, signing a two-and-a-half-year deal with an option for a further 12 months.
United paid £9.6m to Sporting CP to hire the Portuguese coach.