According to Spanish outlet ABC, Real Madrid are looking to snap him up on a bargain deal when the transfer window reopens.
The 28-year-old German international is nearing the end of his contract at Stamford Bridge and he will be a free agent next summer. The player has recently been linked with Bayern Munich as well.
Rudiger will be allowed to negotiate with foreign clubs and he could secure a pre-contractual agreement with Real Madrid in a few months.
The 28-year-old has been exceptional for Chelsea since the arrival of Thomas Tuchel and he has established himself as the best centre back at the club right now.
Apparently, the Spanish La Liga giants are looking to improve their defensive options after the departure of Sergio Ramos and Raphael Varane during the summer transfer window and they have identified the Chelsea player as an ideal candidate.
Real Madrid signed David Alaba on a free transfer from Bayern Munich at the start of the season and they are hoping to partner him with Rudiger soon.
Apparently, the German defender has been offered a new contract at the London club but he has not accepted the proposal yet. Rudiger has been offered 11 million per season and the new deal would more or less double his current earnings. However, the player will not make a decision regarding his future based on the financial side of things and he is more concerned about the sporting vision.
A move to Real Madrid would undoubtedly be a tempting proposition for most players and it remains to be seen whether Rudiger is willing to complete a move to Santiago Bernabeu in the coming months.
The 28-year-old has developed into a key player for club and country and there is no doubt that he has the quality to play for a club like Real Madrid.