The Germany international sees his Stamford Bridge deal expire in the summer of 2022 and is free to discuss pre-contract agreements with other clubs from January onwards.
Now, transfer expert Pedro Almeida has dealt a blow to Chelsea's hopes of a renewal, posting on social media: "At this moment, negotiations between Real Madrid and António Rudiger are advanced. Chelsea still hasn't given up on renewing the German player's contract."
Los Blancos are supposedly willing to offload up to four players in order to fund a move for Rudiger, whose wage demands are thought to be presenting a roadblock in contract talks with Chelsea.
The 28-year-old has played the full 90 minutes in 10 Premier League games this term and has won the Champions League, Europa League and FA Cup during his time with the Blues.