Sky Sports says United's new co-owner Sir Jim Ratcliffe has given the green light to pay in excess of 100m for the midfielder this summer.
Neves, 19, broke into Benfica's first team last season.
Advertisement
Advertisement
The Portuguese played 17 games in the league, of which six were from the start. This season, Neves has taken further steps.
So far, the midfielder has accounted for two goals and two assists in 24 league games.