The Brazilian star is believed to stuck in contract negotiations with the Parc des Princes giants, which are stalling over a wage dispute.
While Moura wants a salary of £4.3m-per-year, the Ligue 1 champions are reluctant to pay him more than £2.8m, which has resulted in a stand-off.
And to make matters worse for PSG, United have been alerted.
The Red Devils are believed to be plotting a big summer of transfer activity, with Louis van Gaal looking on course to seal the club’s return to the Champions League after a season’s absence.
The Old Trafford giants were admirers of Moura back in 2012, but failed to lure him from his homeland to the North West of England as he instead chose Paris.