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Spanish outlet Cadena SER reported that Getafe were left unhappy about the incident after full-time at the Coliseum Alfonso Perez.
They reportedly requested that the referee Ricardo De Brugos Bengoetxea include Bellingham's alleged slur in his official match report.
The alleged verbal spat occurred when the 20-year-old midfielder strongly tackled Greenwood near the touchline, forcing the ball out of play.
TV cameras then picked up Bellingham saying a two-syllable word towards the Getafe forward with a stern look on his face. However, the audio didn't pick up what was said and it remains unclear if any slur was uttered.
La Liga have since released a statement confirming they were investigating the incident, appointing a lip reader to determine whether Bellingham called Greenwood a "rapist".
A statement read: "Getafe yesterday transferred the complaint to the La Liga match director.
"La Liga, as it always does on these occasions, has requested an expert report on lip reading to investigate the matter and act on the basis of what can be proven beyond doubt (by the lip reader)."
Bellingham, if found to have called Greenwood a "rapist", could be handed a potential suspension by the Spanish top flight.
But Spain-based journalist Jose Felix Diaz has claimed that Greenwood doesn't want any trouble while he kickstarts his career at Getafe, suggesting he won't push for Bellingham to be punished.
The former United No. 11 was arrested amid allegations of attempted rape, assault and controlling and coercive behaviour in January 2022 and was later charged. Greenwood denied all accusations.
In February 2023, the Crown Prosecution Service dropped all charges against Greenwood due to a withdrawal of key witnesses and new material coming to light.
