The Blues have allegedly held talks with the centre-back over a new three-year deal at Stamford Bridge.
However, according to Sky Sports News, both Bayern and Dortmund are 'admirers' of the 27-year-old, who spent time in the BVB youth system before moving to Stuttgart.
Rudiger, whose existing deal with Frank Lampard's side has little over two years left to run, has missed a lot of football this season due to injury but returned to the fold in the latter stages of 2019.
The centre-back has made over 100 appearances for Chelsea since arriving from Roma in 2017.
Rudiger has also been capped on 30 occasions by the German national team and represented his country at the 2018 World Cup.