The 22-year-old joined the Spanish club on a season-long loan deal last summer after Man United decided to sanction his departure following an internal investigation.
The Red Devils opened their own investigation after charges of attempted rape, assault occasioning actual bodily harm and engaging in coercive and controlling behaviour were dropped in February 2023.
Man United were allegedly leaning towards keeping Greenwood, before a public backlash contributed to their decision to send him out on loan.
Getafe hold talks over new loan deal
Despite missing a penalty in Friday's defeat to Athletic Club, Greenwood has enjoyed a productive season with Getafe, scoring eight goals and providing six assists in 29 La Liga appearances.
With Greenwood's loan spell coming towards an end, Getafe boss Jose Bordalas previously admitted he is unsure about whether the Englishman would return to the Spanish club next season.
A recent report suggested Man United's preference is to sell Greenwood this summer rather than sanction another loan departure.
However, according to The Athletic, Man United and Getafe have begun talks over a potential loan move for the 2024-25 season.
Getafe are exploring the possibility of bringing Greenwood back to the Coliseum after being impressed with his impact in La Liga.
However, they are unlikely to pursue a permanent deal and are aware that Greenwood could look to move to a Champions League club for next season.
What are Greenwood's alternative options?
There is a belief that Man United are prepared to consider another loan switch if they fail to receive a suitable fee for Greenwood this summer.
With Greenwood under contract until June 2025, the Red Devils could trigger the option of an additional year if they allow the forward to leave on loan, as they look to avoid losing him on a free transfer.
Juventus are believed to be leading the race for Greenwood and could make a push to sign him in the summer transfer window.
There has been a suggestion that Man United could use Greenwood in a potential swap deal for Juventus centre-back Gleison Bremer.
Atletico Madrid have also been linked with a move, while the possibility of Greenwood being reintegrated into the Man United squad has not been completely ruled out.