The former Manchester City midfielder has made just four appearances this season for Los Blancos as he struggles to make an impact at the Bernabeu.
Real Madrid playmaker Brahim Diaz has rejected the opportunity to join Getafe on loan, despite the fact he has barely featured for the first team this season.
Brahim has struggled for regular playing time at Santiago Bernabeu since joining the club from Manchester City for an initial £16 million fee in January 2019 .
The 20-year-old featured in 11 domestic matches for the Blancos in the second half of last season, but his development has stalled since the summer.
Brahim has only managed four appearances across all competitions in 2019-20, and has yet to start a single match.
Zinedine Zidane opted to leave him out of his matchday squad once again for Madrid's trip to Coliseum Alfonso Perez to face Getafe on Saturday.
The visitors earned a 3-0 win thanks to a Raphael Varane double and a late Luka Modric effort, which kept the pressure on Barcelona at the top of La Liga.
After the match, Getafe president Angel Torres revealed that the club have enquired over Brahim's availability, with head coach Jose Bordalas a keen admirer of the ex-City playmaker.
Getafe have seen their approach knocked back, however, as Torres told reporters: "We've asked Madrid president Florentino Perez for Brahim."
"Perez told me that they're OK with that, but it depends on what the boy wants - and it seems like he doesn't want to leave Madrid right now. So we'll have to see."
"Our coach likes him; it's a possibility."
Brahim has until the end of the month to perform a U-turn regarding his short-term future, but as it stands, he will remain in the Spanish capital until at least the end of the season.
The midfielder is under contract at Madrid until 2025, with a clause included in his deal which specifies that City will receive 15 per cent of any future transfer fee.
Brahim will be back in contention for a place in Zidane's squad when Madrid face Valencia in their Supercopa de Espana semi-final clash in Saudi Arabia on Wednesday, with the winner set to take on Barcelona or Atletico Madrid on January 12.
The Blancos are due back in La Liga action six days later, with third-placed Sevilla set to arrive at Santiago Bernabeu for a top of the table showdown.