The 19-year-old has been away on international duty this summer with Portugal at Euro 2024 in Germany, where Roberto Martinez's side were fighting for continental glory.
Despite starting the final warm-up fixture, a 3-0 victory over the Republic of Ireland, Neves failed to make a significant impact at his maiden major tournament.
The midfielder only started the 2-0 defeat to minnows Georgia, with Martinez opting to rotate his preferred XI as Portugal were already secured a spot in the knockout stages.
Neves was an unused substitute during the quarter-final clash with France on July 5, when the Selecao played out a goalless 120 minutes before exiting the competition on penalties.
Man United 'end' pursuit of Benfica's Neves
According to Portuguese outlet O Jogo, Manchester United are no longer in the race to secure the services of Benfica youngster Neves this summer.
The report states that the Red Devils are instead focusing their attentions on the acquisition of Paris Saint-Germain midfielder Manuel Ugarte.
It is believed that Benfica are standing firm at their £84 asking price and valuation of Neves, who is set to miss out on a move to the Theatre of Dreams.
With Erik ten Hag's side unwilling to pay a premium price for the 19-year-old, Luis Enrique's troops could swoop in and seal the signature of the Portuguese.
That would then pave the way for 23-year-old Ugarte to make the switch to the red side of Manchester, where the midfielder would at first recover from an unsuccessful Copa America campaign with Marcelo Bielsa's Uruguay.
Man United's transfer state of play
Whilst the hunt for a new midfielder rumbles on, Man United are edging close to the first signing of a new era of ownership under Sir Jim Ratcliffe and INEOS.
It is understood that the Red Devils are set to announce the signing of Joshua Zirkzee from Bologna, who have demanded £42m for the services of the striker.
The Netherlands international enjoyed a stellar term for Thiago Motta's side, netting 11 goals and providing four assists in 34 Serie A matches.
Despite Bologna having Champions League football to look forward to next season, Zirkzee is willing to take a step down to Europa League action in order to sign for Man United.