Gabriel is set to turn 16 and is reportedly not expected to sign a professional contract with Manchester United, opening the door for a major battle between some of Europe's biggest clubs.
The teenager's situation has attracted significant attention because of his potential, with clubs already positioning themselves ahead of his next career move.
Real Madrid and Barcelona had previously emerged as the two most prominent contenders.
Spanish reports had suggested that Real Madrid were in pole position, while Barcelona sporting director Deco publicly denied that the Spanish champions were interested in the youngster.
Financially, Real Madrid's proposed offer has reportedly been viewed as particularly attractive.
However, SPORT now reports that Bayern Munich have entered the race strongly, changing the picture surrounding Gabriel's future.
According to the report, four clubs currently appear to be at the front of the queue: Real Madrid, Barcelona, Bayern Munich and PSG.
Paris Saint-Germain's interest is not new, but the French champions have reportedly taken a more direct step by making their position known to Gabriel's representatives.
SPORT reports that PSG have contacted Ali Barat, the agent who represents the teenager, to communicate their interest and indicate that they would be prepared to make an offer if the player is open to the move.
That approach would put PSG firmly into the competition for one of Manchester United's most closely watched young talents.
Gabriel's situation is particularly significant because his age means that any move would involve the development and registration rules that apply to underage players.
For the clubs involved, the attraction is the possibility of securing a player regarded as having considerable long-term potential before he establishes himself at senior level.
Manchester United will now face the prospect of seeing one of their most highly rated young players attract attention from across Europe.
With Real Madrid, Barcelona, Bayern and PSG all reportedly interested, Gabriel's next move could become one of the more closely watched youth transfers in European football.