Gomes is a product of the Premier League giants' academy and made ten appearances for the senior side before being released in 2020.
He moved to French side Lille, featuring 129 times, and was recently part of England interim boss Lee Carsley's squads.
Gomes' development has caught the eye of new United boss Amorim, who The Sun report is 'behind' a possible move for the midfielder.
Sporting director Dan Ashworth and technical director Jason Wilcox are said to believe that the 24-year-old could be key to their plans.
Amorim is a 'long-term admirer' of Gomes, who's rated at £25million but sees his contract at Lille expire next summer.
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He can therefore speak to clubs in January regarding a pre-contract agreement, with Tottenham another club who are showing interest.
However, United believe they can tempt Gomes to complete a return to the club as a potential long-term option for 32-year-old Casemiro.
The Brazilian's performances have been scrutinised in recent months, particularly after he was at fault for Liverpool's first two goals in their 3-0 win at Old Trafford earlier this season.
Casemiro was substituted at half time for youngster Toby Collyer but has since returned to regular action for United in midfield.
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Galatasaray interested in a summer move for the former Real Madrid star before the Turkish transfer window closed on September 13.
A deal failed to materialise though and Casemiro, who has also been linked with a transfer to Saudi Arabia, has two years left on his deal.
Whilst this doesn't guarantee a departure, he could be one of two midfielders to head for the exit door next summer.
Christian Eriksen sees his contract expire at the end of the season and there are no ongoing negotiations over an extension.
Amorim's opinion on the Dane will be considered though, with the Portuguese boss currently preparing for his first match at United.
His first appearance on the touchline after he permanently replaced Erik ten Hag comes this Sunday when they travel to Ipswich Town.
The 39-year-old will then be tasked with reviving United's Europa League campaign against FK Bodo/Glimt on Thursday night.
A testing festive period awaits him in the coming weeks as December presents fixtures against Arsenal, Manchester City and Tottenham.