Hudson-Odoi now has 18 months remaining on his contract and despite Chelsea's best efforts, it has been claimed that his representatives have no interest in entertaining an extension to that deal.
According to Sky, Bayern and Chelsea have agreed a transfer of $44.6 million, but it is unclear whether Hudson-Odoi would move in the current Bundesliga transfer window, which closes on January 31, or in July.
"Of course he asked me about Germany", Rudiger told reporters after the Blues lost the first leg of their League Cup semi-final 1-0 against Tottenham on Tuesday.
"They've just signed [Christian] Pulisic for £60m and this is one of the best young payers in world football at the moment and he's not going to get any game time".
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Chelsea remain desperate to convince Hudson-Odoi to stay and Maurizio Sarri's decision to start him against Tottenham was part of that charm offensive. "I can advise him but at the end of the day he decides his future".
'You can see it from both sides. We'll see about the rest, ' he said.
Chelsea are set for a busy transfer window beyond deciding the future of Hudson-Odoi, with Alvaro Morata, Davide Zappacosta and Cesc Fabregas all possibly leaving the club this winter.
"So, why wouldn't he think about moving somewhere else if a club like Bayern Munich are in for him?"
Chelsea star Callum Hudson-Odoi has warned the club they risk losing him on a free if they block his wish to join Bayern Munich. The Argentine is now on loan at AC Milan, but the London club want to sign him this January. He has all the tools to become a big player, but he has to work a lot.