The 23-year-old has featured for Les Parisiens in 23 appearances so far this season, following his free transfer move from AC Milan last summer.
The Italian has competed regularly with former Real Madrid goalkeeper Keylor Navas, with the Costa Rican having featured in 25 appearances for the Ligue 1 side across all competitions.
However, L'Equipe are reporting that Donnarumma has been chosen as the undisputed first choice for the 2022-23 campaign, leaving Navas' future at the Parc des Princes in doubt.
Newcastle United and Juventus are said to be interested in a move for the 35-year-old this summer, whilst PSG will also be on the search for any interest in several other goalkeeping options on the books at the club.
Alphonse Areola, Sergio Rico and Marcin Bulka have all been out on loan this season having failed to nail down a regular spot in Paris during their spells in the French capital, and the report suggests that the trio are likely to join Navas in exiting at the end of the season.
The former has been on loan with West Ham United, and manager David Moyes is said to be interested in acquiring the 29-year-old on a permanent deal at the London Stadium, whilst Rico signed for Mallorca on a loan deal until the end of the season back in January.
Meanwhile, Bulka has spent the year with fellow Ligue 1 side Nice, but having been used sparingly by Christophe Galtier, it remains to be seen whether there is an interest in signing the 22-year-old on a permanent deal.