Carlo Ancelotti's side welcomed David Alaba to the club following his exit from Bayern Munich, but the formidable pairing of Sergio Ramos and Raphael Varane was broken up as the two defenders left for Paris Saint-Germain and Manchester United respectively.
Los Blancos also have Eder Militao and Nacho Fernandez capable of featuring in the heart of defence, but the club are expected to be in the market for defensive reinforcements ahead of the 2022-23 season.
According to Fichajes.net, Real Madrid have now drawn up a five-man transfer shortlist comprising Pau Torres, Milan Skriniar, Antonio Rudiger, Marquinhos and Matthias Ginter for next summer.
Rudiger is yet to pen an extension on his Chelsea deal which expires in 2022, but Skriniar is supposedly close to agreeing a new deal with Inter Milan until the summer of 2025.
Torres, meanwhile, remained at Villarreal over the summer despite reported interest from Real and Man United, while Ginter is due to become a free agent next year and recently admitted that he has not been offered an extension by Borussia Monchengladbach yet.
Real Madrid have claimed 13 points from their first five games of the new La Liga season, although they have already shipped seven goals in league action.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen