The 21-year-old is an option to join the Italian outfit on deadline day but only if Sarri agrees to incorporate him in his squad, according to Gianluca Di Marzio.
The two clubs have been in touch over a potential transfer and it is believed that Greenwood remains open to a move to Italy. Although no decision has been made, the process could be expedited if Sarri gives his consent to the deal.
Greenwood is aware that his future lies away from English shores after the Red Devils informed him that he has no place in Erik ten Hag's squad.
He last made a professional appearance in January 2022 before being arrested on suspicion of attempted rape, assault and coercive control. All charges were dropped earlier in February this year and since then the forward has been working in an individual capacity to make a competitive comeback.
Greenwood also reportedly had offers from two Turkish clubs, including one from Besiktas. However, the two clubs have time on their side with the transfer window in Turkey remaining open until September 15.
It is understood that United are ready to loan Greenwood out with a potential purchase clause in the contract which can be activated at a later date.
Greenwood has a contract until 2025 at Old Trafford and if United fail to get a transfer over the line then they will have to pay off the final two years unless a settlement can be reached between the two parties.