The 28-year-old's current contract at Stamford Bridge expires at the end of the season, with talks over a renewal so far proving fruitless.
Rudiger is understood to be open to signing a new deal if his demands are met, while Chelsea are also keen to keep him, but the two parties remain apart in negotiations.
Foreign clubs will be allowed to open talks over a free transfer for Rudiger from January 1, and the Daily Mail reports that they could make him one of the world's best-paid defenders.
Matthijs de Ligt currently holds the title of best-paid defender with a £400,000-a-week contract including add-ons at Juventus, and the report claims that Rudiger could demand close to that sum due to the lack of a transfer fee - something which would usually be in the region of £70m.
The centre-back is currently on £100,000 a week at Stamford Bridge, marking a significant wage increase should he opt for a lucrative deal elsewhere.
Rudiger has continued to play a big part for Chelsea this season despite the uncertainty over his future, scoring two goals in 20 appearances across all competitions. body check tags ::