There is an ongoing internal investigation into Greenwood after charges of attempted rape, controlling and coercive behaviour and assault against him were dropped in February.
The 21-year-old has not featured for United since he was suspended by the club on January 30 2022, after he was initially accused of assault.
The Red Devils are looking for a European club to take the England international on loan for the duration of the 2023-24 season, The Daily Mail reports.
Italy, Spain and Turkey are considered the most likely destinations for the United academy graduate.
Teams in Italy and Spain, however, may be worried about the optics of bringing the forward on board considering the controversy surrounding him. That's despite the legal case being discontinued because of the withdrawal of key witnesses, and the Crown Prosecution Service's belief that there "was no longer a realistic prospect of conviction".
Greenwood has two years left on his contract at Old Trafford, but they may opt to terminate his deal should they rule that he brought the club into disrepute.