The Germany international has established himself as a key member of Tuchel's backline over the past 18 months, but he is now in the final year of his contract with the Champions League holders.
Rudiger has previously talked up the prospect of signing a new deal at Stamford Bridge, but a recent report claimed that the Blues are struggling to convince him to put pen to paper.
Now, La Colina de Nervion claims that Chelsea director Marina Granovskaia is prepared to part ways with Rudiger in January should no contract resolution be reached, with Paris Saint-Germain, Bayern Munich and Real Madrid all keeping a close eye on developments.
The report adds that Rudiger's sale could lead Chelsea to reignite their interest in Sevilla's Jules Kounde, with manager Julen Lopetegui confirming that a suitable offer for the Frenchman did not arrive in the summer.
Rudiger has played every minute of Chelsea's 2021-22 Premier League campaign so far and boasts seven goals from 155 appearances for the Blues in all competitions.