The Old Lady have reportedly tabled Tim Weah, Douglas Luiz and Dusan Vlahovic as possible options in a swap.
Amorim is believed to want a striker, a midfielder and a wing-back once United complete a planned deal for Bryan Mbeumo with funds generated from player sales.
The scope of a swap deal could increase if Juventus struggle to meet the Red Devils' valuation of between £20m and £25m.
According to GIVEMESPORT, United's discussions with Juve have been positive, and the feasibility of a transfer is set to come to light this week.
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It's claimed that Luiz, the former Aston Villa midfielder who arrived in Turin last summer, has been mentioned during the talks.
United are said to have shown some interest in the 27-year-old amid their desire to bolster Amorim's engine room.
The Old Trafford outfit's priority will be to offload Sancho, though, with the start of pre-season adding to the pressure to push business through.
United's first pre-season friendly takes place against Leeds United in Stockholm on July 19 before the club flies out to America.
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Amorim will be desperate to have Mbeumo through the door before the tour, which features games against Everton, Bournemouth and West Ham United.
He is also sure to want to reshape his squad further before then by overseeing the exits of Sancho, Rashford and their band of outcasts.
With no European football on the agenda this season, Amorim can run with a thinner squad than last term.
Therefore, if United seal a deal for Mbeumo, player sales are expected to be the primary focus, and Sancho's seems like one of the most advanced.