Hudson-Odoi is a valued asset at Stamford Bridge, but the youngster is questioning his long-term future at the club despite his age, having earned only two competitive starts under Maurizio Sarri this season.
Chelsea are still hopeful that they can tie down the forward to a new five-year contract, as previously revealed by Goal, but a serious offer from a big overseas club could tempt the Blues to cash in on a player who is eager for playing time and out of contract in 18 months.
Dortmund's approach for Hudson-Odoi came during Chelsea's talks with the club over Christian Pulisic's availability, with the German side's offer of a swap deal rejected by the Blues as they aim to tempt the player to put pen to paper on a new deal in January.
It is understood that Bayern have a clear plan set out to bring the England youth to the Allianz Arena, the Bavarians eager to add some youth to their forward line as veteran wingers Franck Ribery and Arjen Robben enter the final years of their career.
Juventus and Real Madrid also retain an interest in Hudson-Odoi, who brought himself to the attention of clubs all around Europe since helping Chelsea's academy team to a stunning quadruple in the 2017-18 season.
The Blues are also keen to hold on to goalkeeper Marcin Bulka, who is regarded as the best young shot-stopper currently on the London club's books.
They have, however, already cemented deals for fellow keepers Nathan Baxter and Jamie Cumming to ensure talent continues to come through between the sticks.