Blues head coach Thomas Tuchel is considering his options in the transfer market after guiding the West London outfit to the Champions League trophy.
Sule, who was not always a regular under Hansi Flick, has allegedly been placed on the shortlist of possible arrivals at Stamford Bridge.
However, according to Bild, newly-appointed Bayern boss Julian Nagelsmann is keen to hand the 25-year-old a new contract.
The Germany international currently has 12 months remaining on his contract, leaving Bayern in a position where they are keen to avoid a similar situation to what they have just experienced with Real Madrid-bound David Alaba.
The Bundesliga champions are reportedly happy to hand Sule a one-year extension on his existing terms, keeping him at the Allianz Arena until 2023. body check tags ::