Los Blancos could end the 2023-24 season with three pieces of silverware, having already clinched the league title and the Spanish Super Cup.
The Spanish giants will have the chance to claim their 15th Champions League trophy when they face Borussia Dortmund in next month's final.
Despite losing just two competitive games this season, Real Madrid are still expected to strengthen their squad ahead of the 2023-24 campaign.
Brazilian starlet Endrick will join the club this summer, while French forward Kylian Mbappe is set to arrive on a free transfer when his Paris Saint-Germain contract runs out at the end of June.
Real Madidrd cool interest in Davies, Yoro
There has also been speculation suggesting Real Madrid will look to bolster their backline, with Los Blancos believed to be looking at signing a new centre-back and a new left-sided defender.
Having emerged as a potential target, Davies recently refused to rule out the prospect of joining Real Madrid this summer of when his current Bayern contract expires in 2025.
Carlo Ancelotti's side have also been linked with 18-year-old Yoro, who appeared to be heading towards a summer move to the Santiago Bernabeu.
However, according to COPE, Real Madrid are cooling their interest in Davies and Yoro after turning their attention to alternative options.
Marin, Gutierrez to strengthen Real Madrid's backline
Instead of signing Davies, the report claims that Real Madrid will look to re-sign Girona full-back Miguel Gutierrez.
After rising through the youth ranks at Real Madrid, Gutierrez completed a switch to the Catalan club in the summer of 2022.
However, the deal contained a buy-back clause, which Los Blancos could decide to exercise this summer before deciding whether Gutierrez or Fran Garcia will challenge Ferland Mendy for the left-back position next season.
With Nacho Fernandez set to leave this summer, Real Madrid are expected to integrate 21-year-old centre-back Rafa Marin into the squad.
The young defender has gained valuable experience this season, having made 32 La Liga appearances during a loan spell with Alaves.
Utilising Marin will help Real Madrid save funds and provide cover to their current central defensive options of Antonio Rudiger, Eder Militao and David Alaba.