The 18-year-old has been linked with a move to Old Trafford in recent months after he was constantly being tracked by the club.
Benfica were said to have demanded £47million in order to open negotiations over a move for the player, but United were not willing to meet the mentioned fee.
However, it is now believed that the Premier League side have agreed to pay £40million for the Portugal international as they look to reinforce their squad in the summer.
They could lose veteran midfielder Michael Carrick at the end of the season as he is yet to open talks over a new deal, with Sanches now seen as the perfect long-term replacement.
He has already featured 38 times in all competitions for his side this term, so far managing to score six goals while providing another one assist.