The arrival of the 19-year-old winger, who has made four appearances for the Portuguese second division club, will be confirmed soon.
Oliveirense communication director António Jose Leite has revealed that Amorim's move to Old Trafford in "90 percent complete" and remains confident that the deal will go through.
"He had been promoted to the main squad but [United's] scout was alert and chose to take him there", Jose Leite said.
"At this time the business is 90% done and he can have an excellent contract".
Both A Bola and O Jogo claim the player is now having a trial at the club and should be signing a contract with Manchester United soon.
Although Manchester United are only expected to pay Oliveirense a fee for training rights, the deal is seen well in Portugal, especially because it's expected the partnership could provide a good interchange relation between the two clubs. These details are not yet defined. "Future sales of the player mean guaranteed earnings".
The Red Devils have done well to poach top talent from Portugal in the past, and have used their connections once again as they look like bringing in a potentially exciting talent for the future.
Lukaku could make his United debut, along with Nemanja Matic and Victor Lindelof, on Sunday when United begin their Premier League campaign at home to West Ham.
The Belgium worldwide and the Serbian midfielder arrived at Old Trafford from Everton and Chelsea respectively.