Rudiger, as it stands, will be able to talk to Los Blancos in January, with the Germany international yet to sign a new contract with the Blues.
Alexander-Arnold, on the other hand, still has four years left to run on his contract at Anfield, but Los Blancos are thought to be keen to explore the possibility of signing the 23-year-old.
Here, Sports Mole looks at how the capital giants could line up next season if they manage to sign both defenders from the Premier League during next summer's transfer window.
The departures of Sergio Ramos and Raphael Varane over the summer have undoubtedly left Real Madrid short of options in the middle of their defence, so it is not a surprise that they are so keen on Rudiger.
The German will be one of the most attractive free agents on the market if he does not sign a new deal at Chelsea, and Real Madrid appear to be in prime position to land the 28-year-old, who could slot in alongside David Alaba in the middle of the defence.
Alexander-Arnold, meanwhile, would take up the right-back spot at the Bernabeu, and the 23-year-old would arguably be able to post even better attacking numbers with Los Blancos, as he is likely to have more time on the ball in La Liga.
The England international's defensive qualities at the highest level continue to be questioned, but there is no doubting that he is one of the best attacking full-backs in world football, which makes him a perfect fit for Ancelotti's side.
Elsewhere, Mbappe could arrive to join Karim Benzema and Vinicius Junior in a front three, while Casemiro, Toni Kroos and Federico Valverde could start next season as the first-choice midfield three, with Eduardo Camavinga and potentially Aurelien Tchouameni - if he arrives from Monaco - rotating into the side.