Chelsea have reportedly rejected a pair of bids from the German champions, including Bayern's £35-million offer earlier this month. But the English club's attempts to keep Hudson-Odoi could ultimately prove futile, as the 18-year-old has yet to sign a five-year contract the Blues offered him last summer.
Although Bayern have been unsuccessful thus far, the club's sporting director, Hasan Salihamidzic, reiterated their interest and revealed that discussions with Chelsea are ongoing.
"We want to sign the player," he told German magazine Sport Bild, as translated by FourFourTwo.com. "I am fully convinced of his abilities; we are in talks with Chelsea.
"Both (Benjamin Pavard and Hudson-Odoi) are not finished players yet, but we have many leaders in our team, that's why it would not be a problem if no player came in the transfer window.
"We have to find a good mix between young talents and experienced leadership players."
Chelsea manager Maurizio Sarri criticized Bayern's approach last week, calling the German club "unprofessional" for publicly revealing their interest in Hudson-Odoi, who is under contract until 2020.
After beginning the season as an afterthought in Sarri's plans, Hudson-Odoi's opportunities seemingly increased after news of Bayern's interest emerged last month; he's appeared in four of Chelsea's last six matches in all competitions.