According to Tuttosport (h/t Sam Wilson of Calciomercato.com), the Milan giants are keen to sign the Spain forward, who endured a mixed debut term at Stamford Bridge last season. So much so, they are ready to offer star goalkeeper Donnarumma as part of the transfer package.
Milan are keen to strengthen their attack, and with Blues goalkeeper Thibaut Courtois strongly linked with a move to Real Madrid, the transfer would make sense for both parties.
As Wilson noted, Morata has been linked with a return to Juventus this summer. However, with Cristiano Ronaldo's arrival to join the likes of Gonzalo Higuain, Paulo Dybala and Mario Mandzukic, the Bianconeri are well stocked with high-class attacking players.
Milan are said to have targeted Lazio striker Ciro Immobile earlier in the transfer window but have opted against pursuing the player, having been quoted a price of €100 million (£89 million) for the Italy international.
Morata appears to have emerged as an option as a result, and the Blues are considering moving the player on to make way for Higuain:
Chelsea also have issues to resolve in goal, as Courtois continues to be linked with a move away from the club.
The Belgium international has less than a year remaining on his deal at Stamford Bridge, and it consequently appears a move to Madrid is on the cards. Kristof Terreur of Het Laatste Nieuws reported that while Courtois is in the Spanish capital, no deal will be done until Chelsea find a replacement.
With that in mind, signing a young goalkeeper with Donnarumma's pedigree may be to the benefit of the Blues, especially at the expense of losing a forward who struggled to adapt to the English game last season.
Last term was an admittedly difficult for the Milan goalkeeper, as these figures illustrate:
Still, there were caveats to his poor form. At the start of the 2017-18 campaign, it was announced he would be leaving the club, sparking an angry reaction from some sections of the Milan fanbase; the 19-year-old then went on to agree a new contract at the San Siro.
Despite this, there were still protests against the player, with Milan fans unfurling a banner that told the teenager to "get out" of the club in December. Donnarumma was in tears and had to be consoled by captain Leonardo Bonucci.
Given what has been a turbulent time for the youngster, perhaps a move would be to his benefit. New Chelsea manager Maurizio Sarri, formerly of Napoli, would have seen firsthand just how talented the Italy international is when he's at his best too.