Despite emerging as a key player in Thomas Tuchel's Blues side, the Germany international has less than a year remaining on his contract.
According to BILD, Rudiger's preference is to renew his deal at Stamford Bridge over the coming weeks after helping Chelsea to win the Champions League last season.
However, the report claims that Bayern have been in contact with Rudiger's brother and representative Sahr Senesie over a transfer in 2022.
Should Rudiger fail to agree fresh terms with the Premier League giants before the end of the year, he will be entitled to open formal discussions with any interested parties.
Bayern are assessing the market for potential additions in defence with Niklas Sule's contract also due to expire at the end of the campaign.