The 20-time English champions have identified Amorim as their number one target to replace Erik ten Hag as head coach, and it is understood that the 39-year-old has already agreed personal terms at Old Trafford.
However, a move is complicated due to the 30-day notice period in his Sporting contract.
Man United have signalled a willingness to pay his buy-out fee of €10m (£8.3m), but the Green and Whites allegedly want a further €5m (£4.2m) to let him leave now, with that also including compensation for Carlos Fernandes, Adelio Candido and Jorge Vital.
According to talkSPORT, Amorim is expected to remain with Sporting until November 10, meaning that he would take charge of three more games against Estrela, Manchester City and Braga.
Man United, Sporting 'could make Amorim announcement on Thursday'
The report claims that an announcement could both clubs could be made on Thursday, and sports scientists Paulo Barreira and Emanuel Ferro are also likely to follow Amorim to Old Trafford.
Amorim's first game in charge of Man United could therefore come against Ipswich Town on November 24, with Ruud van Nistelrooy set to remain in charge of the Red Devils on an interim basis until the November international break.
Van Nistelrooy guided Man United to a 5-2 success over Leicester City in the last-16 stage of the EFL Cup on Wednesday night.
Bruno Fernandes and Casemiro both netted twice, while Alejandro Garnacho was also on the scoresheet, as the Red Devils booked their spot in the quarter-finals with a impressive victory in their first game since Ten Hag's departure.
What has Amorim said about his future?
Amorim was asked about his future after guiding Sporting to a 3-1 victory over Nacional in the Taca da Liga on Tuesday night.
"Nobody knows if it was a farewell match or if there will be a farewell. It's a matter that hasn't been decided yet. Let's analyse the match," Amorim told reporters after the contest.
Sporting won the Primeira Liga title in 2020-21 and 2023-24 under Amorim's management, in addition to three cups, and he is viewed as one of the best young managers in world football.
Man United have three more games before the November international break, taking on Chelsea and Leicester in the Premier League either side of a home Europa League fixture against Greek outfit PAOK.