Amorim - who will officially take over as Erik ten Hag's replacement during the next international break - has overseen the development of the 17-year-old into one of Europe's most promising right-backs this season.
Quenda had never made a senior appearance for Sporting before this season, but he has already played 16 times in the current campaign, coming up with two goals and an assist in the process.
The 2007-born protege has started eight games in the Primeira Liga and two in the Champions League for Sporting, and he is expected to make the first XI against Manchester City on Tuesday.
Amid growing interest in his services, Sporting tied Quenda down to a new long-term deal back in September, and the teenager's current terms are thought to include a release clause worth £83.9m.
PSG 'among Man United's main competitors' for Quenda
Man United's interest in the defender is not thought to have dwindled since his extension, as recent reports have claimed that they have been sending scouts to keep an eye on his progress in his homeland.
However, Foot Mercato claims that a number of other top continental teams are running the rule over Quenda, including Paris Saint-Germain, who reportedly tried and failed to sign him before Sporting tied him down to new terms.
PSG currently possess one of the best right-backs on the planet in Achraf Hakimi, who is soon expected to sign a new deal at the Parc des Princes, but he is allegedly on the radar of Man City, Real Madrid and Liverpool.
Even if Hakimi stays at PSG as expected, Quenda could arrive as an understudy to the Moroccan, while Man City are also following developments amid claims that they could sell Kyle Walker for just £15m next year.
PSG apparently feel that they have a trump card in Jorge Mendes, Quenda's agent, who has helped broker deals for Vitinha, Joao Neves and Bradley Barcola to join the Ligue 1 champions in recent times.
RB Leipzig and Juventus have also been credited with an interest in the 17-year-old, but the latter are not expected to be serious contenders due to their lack of financial firepower.
What other Sporting players could Amorim target?
Amorim has insisted that he will not be making any moves for his current Sporting stars in January, but that has not stopped the rumour mill from swirling, especially given the talent at the 39-year-old's disposal.
One name persistently linked with a move to the Premier League has been Viktor Gyokeres, the Swedish striking sensation who has already scored 20 goals this season, including four in one game against Estrela Amadora.
Highly-rated centre-backs Goncalo Inacio and Ousmane Diomande are also believed to be on the radar of the Red Devils, as is midfielder Morten Hjulmand, who memorably scored a long-range rocket for Denmark against England at Euro 2024.