Neves has two years left to run on his contract, but Wolves are prepared to cash in on him in the ongoing transfer window.
The Portugal international is also keen to move on and test himself at a bigger club leading to speculation that his departure is an inevitability this summer.
Arsenal emerged as early favourites to sign Neves and the Gunners are believed to be considering taking him to the Emirates as the replacement for Granit Xhaka.
But Manchester United have entered the race to sign Neves as well and it has been claimed that they have moved ahead of the Gunners in the race.
The Premier League giants are now focused on getting a deal over the line to sign Raphael Varane from Real Madrid at the moment.
But signing a midfielder is also on their agenda and a number of players are on their shortlist.
Neves is Premier League proven and Manchester United are considering tabling a bid for him this summer.
Unlike Arsenal, Manchester United are in a position to offer him the prospect of playing in the Champions League next season.
Wolves are ready to sanction his sale if they receive a fee of around £35m this summer.
