Diaz signed a six-and-a-half-year contract at Madrid when he joined for an initial £15 million ($19m) from Manchester City last January, but he has hardly featured since.
The 20-year-old has only made five appearances this season, though he did recently score in the 3-1 Copa del Rey win over Unionistas on January 22.
Getafe had offered him a route out of Santiago Bernabeu on loan, but their manager Jose Bordalas says they were turned down.
Asked if Getafe had been interested in Diaz, he told reporters: “Getafe wanted him, and Bordalas wanted him as well because he is a great player.
“Brahim informed Real Madrid of his intention to continue with them because he is confident that his opportunity will come.
“I would like to have had him here with us, he would have been a very good addition.
“Players go where they want to be. Brahim is at Real Madrid. Having made his intention clear, we have to respect him.”
Diaz’s departure was a disappointment for many at Manchester City, with the Spaniard far from unique in leaving the Etihad Stadium after coming through the youth system.
When he made his debut against Leganes shortly after, he said it was the fulfilment of a childhood dream. Later, Zinedine Zidane would hail his “fearless” display as the only bright spot in a dismal display against Getafe last season.
However, while Diaz does not seem to believe his dream has ended, it has certainly stalled.
An abdominal injury curtailed his start to the 2019-20 campaign after a hamstring issue did for most of his pre-season, and he has played just 23 minutes in La Liga as a result.
Diaz has been on the bench for two of Madrid’s last four league games, perhaps offering some hope that his chance is yet to come.
He may be hopeful of featuring in Madrid’s Copa del Rey last-16 game at Real Zaragoza on Wednesday, which is followed by a home derby against Atletico Madrid.
Zidane’s side then have three more league fixtures to negotiate before the first leg of their Champions League clash with Manchester City on February 26.