The Portuguese has struggled to agree a new deal at Old Trafford, with his high wage demands proving a stumbling block.
According to The Mirror, PSG would be willing to give him the £100,000-per-week that he wants and believe that they could get Nani for as little as £10m.
It is thought that the winger would prefer a move to Spain after rejecting a move to Russia last summer, but is willing to talk to PSG.
Red Devils manager Sir Alex Ferguson is keen for the winger to sign a new deal but is unwilling to match his demands.
Nani, whose current deal runs out next summer, has apparently told United that he would not be afraid to see out his contract and leave for free.