The Belgian's current deal at Old Trafford expires next summer and he is yet to pen a new deal with the club.
With Fellaini seemingly unsettled, 'Le10Sport' claim that PSG, who are in desperate need of a defensive midfielder, have added him to their transfer shortlist.
They are eyeing a potential cut-price deal for the 30-year-old and move would see him join the French club on a four-year deal.
Fellaini has played an important role for Jose Mourinho either side of his knee injury suffered in October, but negotiations for a new contract appear to have stalled, meaning the midfielder is looking more and more likely leave next summer.