Man United are expected to sign at least one central midfielder this summer, with Casemiro and Christian Eriksen both potentially moving on, while Donny van de Beek is set to leave the club.
A permanent deal for Sofyan Amrabat is also seen as unlikely, with the Morocco international finding it difficult to make a strong impression since arriving on loan from Fiorentina.
Neves is believed to be Man United's leading target in that area of the field, with the 19-year-old thought to have been consistently scouted by the Red Devils over the last year.
However, according to journalist Bruno Andrade, Benfica are likely to demand that his full €100m (£86m) release clause is paid in order for him to leave.
Man United 'could be priced out of move for Neves'
Andrade claims that Benfica will not enter into any transfer discussions before Euro 2024, as they believe that clubs will be willing to pay his buy-out fee if he impresses for Portugal at the tournament.
The teenager has been a vital player for his club during the 2023-24 campaign, making 55 appearances in all competitions, scoring three goals and registering two assists in the process.
Neves has three goals and two assists in 33 league appearances this term, while he also played six times in the Champions League and six times in the Europa League before Benfica were eliminated from both competitions.
The midfielder has already played 75 times for his current side, scoring four goals and registering three assists, and he is viewed as one of the best young talents in European football.
Is a summer deal for Neves realistic?
At €100m (£86m), it is very unlikely that Man United will be able to sign him this summer.
The Red Devils are facing missing out on European football altogether for next season, which will impact their transfer budget, and they do need to sell this summer in order to buy.
Man United are expected to be active, but they are also likely to bring in two centre-backs and a centre-forward, so it is difficult to imagine them paying out such a large amount on one player.
The 20-time English champions are believed to be hopeful that Neves's price could be negotiated down, especially with the youngster said to be keen on a switch to Old Trafford.
However, the Red Devils are not the only club interested, with Manchester City, Liverpool and Chelsea also believed to be keen on his signature in the upcoming market.