Los Blancos decided against battling Manchester United for Leny Yoro in the latter stages of the English club's negotiations with Lille, so the Spanish outfit have missed out on his signature.
Further acquisitions this summer have not been ruled out, though, as there is money to spend.
Real Madrid will be one of the teams keeping a close eye on the Paris 2024 Olympics, with the football tournament due to begin on July 24.
With that in mind, Sports Mole takes a look at three players from the competition that Carlo Ancelotti's side could potentially target.
Julian Alvarez (CF | Argentina Under-23s | Manchester City)
Alvarez's future is currently the subject of much speculation, with the 24-year-old believed to have told Man City that he is ready to seek a move during this summer's transfer window.
The forward is not a guaranteed starter at the Etihad Stadium due to the presence of Erling Haaland, which has allegedly led to him considering his options.
The Argentine has scored 36 goals and registered 18 assists in 103 appearances for Man City, including 19 goals and 13 assists in 54 appearances during the 2023-24 campaign.
Mbappe is expected to play through the middle for Real Madrid next season, but he is not a centre-forward, and it is an area that Los Blancos might need to address sooner rather than later.
Miguel Gutierrez (LB | Spain Under-23s | Girona)
Gutierrez represented Real Madrid's youth academy between 2011 and 2020 before progressing to senior football, and he made 10 appearances for the capital outfit's first team before a switch to Girona.
The 22-year-old has been outstanding for Girona over the last two seasons, with his performances during a famous 2023-24 campaign for the Catalan outfit particularly catching the eye.
Man United are among the clubs to be linked with Gutierrez, but it has also been suggested that Real Madrid could bring him back to Bernabeu this summer to provide support for Ferland Mendy next season, with a deal for Bayern Munich's Alphonso Davies unlikely at this stage.
Real Madrid are thought to have the option to re-sign Gutierrez for just €8m (£6.7m) this summer, so it could potentially be one of the biggest bargains of the summer considering his quality.
Thiago Almada (AM | Argentina Under-23s | Botafogo)
Almada's career is an interesting one, having left Velez Sarsfield for Atlanta United in 2022, and he represented the MLS outfit on 83 occasions, scoring 26 goals and registering 34 assists.
The 23-year-old joined Brazilian outfit Botafogo earlier this month, but it is not impossible that he could make the move to a major European club in the near future.
The attacking midfielder has a record of 50 goals and 34 assists in 183 career appearances, and he certainly appears to have the skillset required to turn out fo a team of Real Madrid's ilk.
A number of clubs will be having a close look at his performances for Argentina this summer, and it might well be that Botafogo are only able to keep hold of him for a year or so.