The new Portuguese manager, who took over after Erik ten Hag was let go, made his first appearance at the club's Carrington training complex on Monday. His arrival came after a successful 4-2 win in his last game coaching Sporting Lisbon.
On Friday, United released a short clip from Amorim's first interview with the club's in-house TV channel showing him looking around a floodlit Old Trafford.
"You watch on TV and you know that it's big and it's impressive, but when you are here you can feel it and I think you feel the history," Amorim said.
"I'm really, really proud to be a Manchester United coach, so it's amazing. It's a real honour to be here."
Told by the interviewer that there is a "weight to the place but it does lift you up", Amorim added: "That's really funny because I feel very relaxed.
"Maybe because it's not gameday. When we have a game I'm a different guy but I really don't feel the weight.
"I'm really excited and I'm quite relaxed you know. I think I am where I am supposed to be. That's the feeling."
Amorim's first match in charge will be away at struggling Ipswich on November 24, following the international break.
United are 13th in the Premier League table after a poor start to the season but are only four points off the top four.
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Ruud van Nistelrooy, put in temporary charge of United after Ten Hag's dismissal, on Friday issued an emotional farewell message to the club, where he also starred as a striker.
The former PSV Eindhoven boss, appointed as an assistant coach in July on a two-year contract, had voiced a desire to stay at Old Trafford under Amorim.
But United issued a statement on Monday confirming the 48-year-old would not be part of the new coaching set-up.
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