On Friday, Man United confirmed Amorim's arrival, but he will not officially begin work at Old Trafford until the November international break, with Sporting fighting to keep him for the upcoming games with Manchester City and Braga.
Amorim has already confirmed that he will not be targeting any Sporting players in January, but according to The Sun, the 39-year-old has a number on his radar for next summer's transfer window.
The report claims that Viktor Gyokeres, Goncalo Inacio, Ousmane Diomande and Morten Hjulmand could be targeted by the 20-time English champions in 2025, with Amorim convinced that all four could have an impact at Old Trafford.
Gyokeres has scored 63 goals and registered 19 assists in 66 appearances for Sporting since his arrival from Coventry City in the summer of 2023, including 20 goals in 16 outings during the 2024-25 campaign.
The Sweden international addressed his future after scoring four times for Sporting against Estrela Amadora, telling reporters on Friday: "I don't know, I'm here. I really like being here, it's not something I think about. I'm enjoying it here."
Gyokeres, Inacio, Diomande, Hjulmand 'on Man United's radar'
Centre-backs Inacio and Diomande are also reportedly of interest, with the pair proving to be important players under Amorim.
Inacio was heavily linked with Liverpool during the recent transfer window, while Man United were also thought to be keen on the Portugal international over the summer before deciding to focus their attention on Leny Yoro.
Diomande, 20, is viewed as one of the best young centre-backs in world football, with Arsenal, Chelsea, Liverpool and Newcastle United all believed to be keen on him, but there is a €80m (£67m) release clause in his contract.
Yoro, Matthijs de Ligt and Lisandro Martinez are expected to be important defensive players under Amorim, but Harry Maguire, Victor Lindelof and Jonny Evans could all leave the club at the end of the campaign.
Maguire, Lindelof and Evans are all out of contract next June, although the club have the option to activate a 12-month extension in the former's contract, and he is the likeliest of the three to stay for another season.
Hjulmand could solve Man United's midfield issues
Man United are expected to sign a ball-playing central midfielder next summer, with Christian Eriksen's contract due to expire, while Casemiro is also being linked with a move away from the club.
Kobbie Mainoo and Manuel Ugarte could be the starting midfield two in Amorim's 3-4-3 formation, with Bruno Fernandes potentially playing further forward, but Hjulmand could have a huge impact at Old Trafford.
The Denmark international has again been a vital player for Sporting this season, making 14 appearances in all competitions, contributing one goal and one assist in the process.
Hjulmand, 25, has a contract with the Green and Whites until June 2028, and his deal also includes a release clause of €80m (£67m), but there have been suggestions that he could potentially be available for a fee in the region of €47.5m (£40m).