The Costa Rica international has spent the past two seasons as PSG’s first-choice keeper, making 80 appearances for the Ligue 1 giants.
However, the French side are expected to shortly announce the signing of AC Milan stopper Gianluigi Donnarumma on a free transfer.
Spanish outlet Marca claims that Navas will look to leave the Parc des Princes once Donnarumma arrives as he is not willing to play second fiddle.
Man United are said to be one of three teams interested in the 34-year-old, along with Serie A pair Juventus and Milan.
Navas, who was previously on Real Madrid’s books for five seasons, only signed a new three-year contract extension with PSG in April.