The Wolves midfielder Neves, 24, has two more years on his current contract at Molineux — but has spoken of his desire to play in the Champions League.
His agent Jorge Mendes has been in contact with United over a potential offer for the Portugal international since the summer with ex-manager Ole Gunnar Solskjaer a big fan.
According to SunSport, Manchester United could bid around € 31million to lure Neves away from the Midlands this month.
However, Wolves are believed to only listen to offers over € 47million for their star — which have also sparked Arsenal interest in the past.
Neves is happy at Wolves, and he’s unlikely to sign a contract extension as he considers the next stage in his development.
United interim boss Ralf Rangnick is on the hunt for a new midfielder after poor performances from Scott McTominay, Nemanja Matic and Fred since joining.
The German coach had a front row seat to Neves’ ability as Wolves claimed a famous 1–0 win over United at Old Trafford on Monday.
Wolves manager Bruno Lage — another Mendes client who replaced Nuno Espirito Santo this summer — is desperate to keep Neves.
Lage said: “It’s not about a contract or the money. It’s about creating a great team that fights for different things.
“Ruben is in this place where he needs a different challenge. And we also want a different challenge for the club. We want to push young guys, like Ruben, to the next level.”
Ruben signed for the Porto Wolves in the summer of 2017, becoming a mainstay of the squad which was promoted to the Premier League a year later before qualifying for Europe.
Asked about his own future in December, Neves added: “The future will soon be visible.
“I like living in the present and I’m happy, I feel good at Wolverhampton and I’m going to focus here because if I do it right I’m sure the future will be bright.”