The 21-year-old has not played a competitive match since January 2022.
He was suspended by United at that point following his arrest on suspicion of attempted rape, assault and coercive control.
United decided at the end of a long-running internal investigation that there was no place for him in their plans at Old Trafford.
According to The Sun, he could now be handed his bow for Getafe in a La Liga meeting with Osasuna on September 17.
A source has told that publication: "The coaching staff have been impressed with his sharpness and plan to throw him in as soon as they can."
Greenwood is still tied to a contract at United through to 2025.
The Premier League club are funding his accommodation in Spain, along with a translator and regular visits from friends and family.
Greenwood took in 129 appearances for United, scoring 35 goals, and has one senior international cap for England.