The 26-year-old is expected to leave the European champions this summer after talks over a new deal at the club broke down.
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PSG have since replaced him with French shot-stopper Lucas Chevalier, who joined from Lille for a reported fee of €40 million plus an additional €15 million in potential bonuses.
United are one of several Premier League clubs said to be interested in signing Donnarumma, who has just one-year left on his deal in Paris.
While signing autographs after their pre-season game against Fiorentina, Amorim was asked about a move for the Italy international, to which he responded with a chuckle.