The 25-year-old has made no secret of his desire to join the Red Devils in the past, admitting that he came close to signing for Sir Alex Ferguson's side in 2012.
Moura has struggled for game time in recent months, making just six appearances under Unai Emery this term and last starting a game for the French giants in May.
The Brazil international was left out of PSG's squad to face Amiens in the Coupe de La Ligue on Wednesday and, according to UOL Esporte, the player is "counting down the days until he leaves PSG".
However, the report goes on to suggest that United want to begin talks at around £18m, while the Ligue 1 side is not willing to do business for less than double that value.
Moura reportedly feels aggrieved by the "exorbitant" valuation placed upon him and thinks that PSG's stance could wreck his move to Old Trafford.
Nantes are also believed to be interested in the winger's services.