He has become a part of Chelsea's first-team squad over the past year, but has still only featured three times in the Premier League, and reports suggest he is refusing to discuss a new contract until he is given assurances over playing time.
Maurizio Sarri named four starlets - Ethan Ampadu, Andreas Christensen, Ruben Loftus-Cheek and Callum Hudson-Odoi, in his starting 11.
"We definitely want to sign him - he has the qualities which would fit very well into our team", Bayern's director of sport Hasan Salihamidzic said on Wednesday at their winter training camp in Doha. "Go back and see how many games Steven Gerrard played when he was 18 years old, right?" A very good match with application, very good in the defensive phase, but he has been completely normal. "I don't want a player as important as Cesc unhappy".
Bayern apparently believe this will further convince Hudson-Odoi how much he is wanted.
"Since my departure from Arsenal I talk every two or three days with Cesc and it has not changed in recent days", he said.
But after Chelsea announced the signing of Christian Pulisic last week, chances for Hudson-Odoi to make an impact in the first team next season are likely to be limited. He can play but of course, sometimes he will be on the bench, like Willian or Pedro, but now I can start to consider him at the same level. It's important because if you have five or six players from the academy you can have soul, more than when you have 25 foreign players'.
The 18-year-old had a good match for the Blues as they lost 1-0 to Tottenham in the first leg of their Carabao Cup semi-final on Tuesday night.
"In my opinion, he's a player who would fit in well at our club".