Ahead of Manchester United's clash with Burnley this weekend, Amorim offered a questionable media preview, declaring he sometimes "hates my players" and also sometimes he feels like "quitting".
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After United's Carabao Cup defeat at Grimsby Town, Amorim's future at Old Trafford has come into sharp focus.
The Times says Benfica presidential candidate Joao Noronha Lopes is monitoring Amorim's situation. Lopes is open to adding Amorim to his ticket.
Amorim won three league titles as a player with Benfica.
Lopes said: "He's an excellent coach, under contract with Manchester United. I won't destabilise Benfica. They have a very important match ahead of them."