Since last June, Pogba has been heavily linked with a move away from Old Trafford, leading to speculation about a switch to Real or Juventus.
The latter, Pogba's former club, are now regarded as the favourites to re-sign the World Cup winner, providing that they can include at least one player in part-exchange.
However, Le 10 Sport suggests that Real and PSG could still decide to enter the race for the playmaker over the coming months.
The report claims that, as it stands, the two clubs have other priorities ahead of the next transfer window, particularly in the case of PSG who are eager to agree new contracts with Neymar and Kylian Mbappe.
Meanwhile, Los Blancos are only likely to re-enter the race for Pogba if president Florentino Perez changes his stance on the France international.