Donnarumma has been increasingly linked with a move away from San Siro since breaking into the Milan first team at the age of just 16, with a number of Europe's top clubs thought to be interested in his signature.
The 19-year-old's agent Mino Raiola has clashed with the Italian giants on a number of occasions, and Donnarumma announced his intention to leave the club last summer before performing a U-turn.
Chelsea could find themselves in the market for a new goalkeeper as Thibaut Courtois's contract expires at the end of next season, with the Belgian thought to be keen on a move to Real Madrid.
Italian outlet Corriere dello Sport reports that Milan could be willing to offer Donnarumma as a replacement for Courtois in exchange for Morata, who endured a disappointing first season at Stamford Bridge and lost his place in the team to Olivier Giroud towards the end of the campaign.
Morata's form saw him miss out on a place in Spain's World Cup squad this summer, and the 25-year-old is thought to be open to the idea of a return to Italy, having previously spent two years with Juventus.