Greenwood departed Manchester United on loan last summer after reaching a mutual agreement with the club that it was best for him to recommence his career elsewhere after he was arrested on suspicion of a number of charges, including attempted rape, in January 2022.
The Crown Prosecution Service subsequently dropped the charges in February 2023, but Greenwood was sent out on loan to Getafe and he has made a positive start to life in Spain.
Thursday's clash pitted the two English players against one another and according to some viewers, it produced unsavory scenes.
After completing a crunching tackle on the 22-year-old, the camera focused on Bellingham, who some fans believed muttered the word 'rapist' in the direction of the Getafe forward.
Jude Bellingham (white) and Mason Greenwood (blue) faced off in the derby clash on Thursday night
Some supporters on social media claimed that Bellingham muttered an insult to Greenwood
The club has asked referee Ricardo de Burgos Bengoetxea to include the words in his report, as well as notifying the LaLiga delegate present at the game to review footage of the alleged insult, according to Cadena SER.
The club is not thought to be looking to make a complaint against Bellingham, but is keen to study the images after a clip of the incident went viral on social media.
The inclusion of the incident in the match report could yet subject Bellingham to a disciplinary procedure from the Spanish football federation (RFEF), but it would likely be difficult to prove that the former Borussia Dortmund starlet had made the statement without accompanying audio.
Bellingham's representatives have been contacted for comment.
Madrid had taken the lead in the 14th minute through Joselu before the former Stoke City forward doubled his tally 10 minutes into the second half.
Carlo Ancelotti's side's victory took them back to the top of LaLiga, two points ahead of surprise package Girona in second.
Madrid welcome cross-town rivals Atletico on Sunday before a top of the table clash against the Catalan club next Saturday.
It came just after the Real Madrid sensation had tackled Greenwood near the touchline
Greenwood was unable to get into the game, despite playing the full 90 minutes
'If we win the next two games we will have six more points and that will be good,' Ancelotti told a press conference.
'Let's hope we can count on Rudiger (for Sunday's derby), I think he can recover. We have two days to try to get him back, it's a strong blow to the thigh.'
Greenwood ended up playing the full 90 minutes against Madrid but was unable to influence the result as Joselu's heroics sealed the win.
The Man United loanee did hit the post just after the break following a shot from outside the area.
Madrid had dominated from the start and Joselu netted a towering header from Dani Carvajal's cross in the first quarter of the game to put the visitors ahead.
He had a great chance to extend Real's lead in the 38th minute, but his shot was saved one-handed by goalkeeper David Soria.
Joselu ended up scoring a brace to seal a vital win for Real Madrid and their title hopes
Already missing regulars including goalkeeper Thibaut Courtois and defenders David Alaba and Eder Militao, Real manager Carlo Ancelotti suffered another setback when centre back Antonio Rudiger did not return after the break due to a leg injury.
Joselu extended Real's lead moments after the interval, slotting home a low strike assisted by a fine pass from Vinicius Jr.
He could have completed his hat-trick when he burst through following a quick counter-attack, but tried to set up Vinicius who chipped the ball straight at Soria from close range.
Soria made fine saves from Federico Valverde and Vinicius and Getafe could have reduced the deficit after Borja Mayoral took advantage of a mistake but Real goalkeeper Andriy Lunin made a brilliant save to deflect his point-blank strike on to the post.
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