The 28-year-old has been a vital player for the Blues since Thomas Tuchel's arrival as head coach, but his contract with the London club is due to expire in June 2022.
According to the Daily Mail, Chelsea are facing 'a major battle' to keep hold of the Germany international, who is seriously considering leaving the Premier League side on a free transfer next year.
The report claims that the Blues have offered a new deal worth £125,000 a week, but there is still no agreement, and Paris Saint-Germain, Juventus, Real Madrid and Bayern Munich are all keeping a close eye on developments.
Rudiger allegedly wants to fully focus on his performances on the pitch and has no plans to sign a new contract in the near future.
The German has played every minute of Chelsea's 2021-22 campaign to date, including the full 120 minutes of the UEFA Super Cup against Villarreal in August. body check tags ::