Gabriel has attracted considerable attention across Europe, with Real Madrid emerging ahead of several major rivals, including Barcelona, Bayern Munich and Paris Saint-Germain, in the pursuit of his signature.
The youngster is regarded as one of the most exciting prospects in English football, and his potential departure would represent a significant loss for Manchester United's academy.
According to journalist Jorge C. Picón, Gabriel's representatives expect the transfer to be finalised next week or, at the latest, the following week.
Real Madrid are understood to have reached a verbal agreement with the player and his representatives, although the move has yet to be formally completed.
The teenager is expected to sign his first professional contract, with the possibility of joining the Spanish club in January.
His age is an important factor in the proposed arrangement. Gabriel turned 16 recently, making him eligible to sign a professional contract in Spain, while the normal minimum age for a professional contract in England is 17.
His European Union passport could also prove significant, with regulations potentially allowing him to move to Spain before the end of his existing academy registration at Manchester United.
However, the situation is not entirely straightforward. United remain entitled to compensation for his development, while FIFA regulations and the necessary registration procedures will have to be satisfied before any transfer can be completed.
Sky Sports reported on November 4 that Real Madrid had reached a verbal agreement with Gabriel, although there had been no direct club-to-club contact at that stage.
The forward had attracted interest from several leading European sides after deciding to seek opportunities elsewhere, with Real Madrid now appearing to be in the strongest position.
For the Spanish club, securing Gabriel would represent another significant investment in youth development. His arrival would add to a recruitment strategy that has increasingly focused on identifying outstanding young players before they establish themselves at senior level.
Manchester United, meanwhile, face the prospect of losing a player they had regarded as one of the brightest talents in their academy.
Although the agreement is not yet official, the indications are that Gabriel's future is increasingly likely to lie in Madrid, with January emerging as the expected timeframe for his arrival.