The reigning Bundesliga champions are pushing hard to sign the 18-year-old, and BBC Sport's Alistair Magowan reports that the feeling is mutual.
Bayern improved their offer to £35 million in early January, leading sporting director Hasan Salihamidzic to publicly state that they "really want" Hudson-Odoi in the winter transfer window.
Chelsea apparently countered by tabling a new contract worth £80,000 a week, but without guarantees over playing time, Hudson-Odoi has decided it would be best for him to leave.
Hudson-Odoi has made just three Premier League appearance this season, and the signing of Christian Pulisic for £58 million cast even more doubt over the future of the English youngster.
Chelsea manager Maurizio Sarri denounced Bayern for approaching a player who's currently under contract, calling their behavior unprofessional and disrespectful.