The Bundesliga champions are considering their options ahead of next season and could make a move for the German if the conditions are right.
The Bundesliga champions join Paris Saint-Germain and Real Madrid in keeping tabs on the Germany international's contract situation at Stamford Bridge.
As previously reported by Goal, the European heavyweights are monitoring Rudiger's situation as he is yet to sign a contract extension with Chelsea and his current deal is set to run out next summer.
How concrete is Bayern's interest?
Bayern have been in touch with Rudiger's agent and brother, Sahr Senesie, but the talks are purely preliminary at this stage.
Julian Nagelsmann's side consider the 28-year-old to be a good replacement for Niklas Sule should the latter choose to move on from the Allianz Arena next summer.
Like Rudiger, Sule's contract expires at the end of the season, and he has put extension talks on hold as he has not yet decided whether he wants to continue with the Bundesliga champions.
There is, however, no hurry for both Sule and Bayern, while Nagelsmann has been pleased with the player's development and feels there is no need for an additional central defender to be brought in if he decides to stay.
What does Rudiger want to do?
Talks are under way between Chelsea and Rudiger regarding a contract extension, although the Blues are remaining cautious over his demands.
The player himself is happy to stay in London but is aware that, given his age, his next contract may well be his final big-money deal.
In addition, interest from Europe's elite and the fact that Thomas Tuchel considers the defender a key member of his squad put Rudiger in a strong negotiating position.
The bigger picture
Should talks with Chelsea break down, Rudiger will of course not be short of options given the magnitude of the clubs monitoring his situation.
The Blues, meanwhile, retain a keen interest in Sevilla defender Jules Kounde, and could return with a bid for the 22-year-old Frenchman in the January transfer window.
Source: Goal
