The Portuguese is currently preparing for his first transfer window as Red Devils boss.
United will be able to add to their options from January 1 through to the deadline at 11pm on February 3.
Former striker Teddy Sheringham has called for his old club to make an audacious move for Declan Rice as a 'statement' signing to kickstart the Amorim era.
Sheringham told Genting Casino: "I said a couple of years ago, Manchester United should have got Declan Rice.
"If they went out and bought Declan Rice off of Arsenal, that'd make me laugh, because that'd obviously make Arsenal weaker and make United even stronger.
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"He's a proper player that leads by example. That's the type of player that you need in your football club.
"When you're making a statement about a new manager coming in and buying new players, that is the type of player you buy. Declan Rice all day."
Rice has been a key part of the Gunners' title challenge so far this year, missing just two of their 16 Premier League matches.
Across 20 appearances on all competitions, the 25-year-old has scored one goal and added four assists from midfield.
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The England international only moved to the Emirates Stadium last summer for a club record £105million.
Meanwhile, his contract runs until 2028 with Arsenal having the option to extend it by a further year.
As well as a move for Rice, Sheringham has also played down a move for Sporting Lisbon striker Viktor Gyokeres.
The three-time Premier League champion added: "I don't think it's imperative for United to move for Viktor Gyokeres at the moment when you've got Rasmus Hojlund.
"I think there's other areas he would prefer to nail down. I think the club need a left back. Luke Shaw's struggling with his injuries. He seems to get one after another, and you can't pin your hopes on someone like that.
"Another really good midfield player would be great, so I think there are other players and other areas to strengthen that are more important to him than buying another centre forward. Hojlund is showing enough."
Gyokeres was signed for Sporting in 2023 by Amorim, scoring 66 goals in 68 appearances under his old boss.
Hojlund, meanwhile, has scored seven times so far this term, with five of those coming since Amorim's arrival.