Chelsea lost their League Cup first leg tie against Tottenham Hotspur 1-0, after a controversial Harry Kane goal.
Bayern have also offered the 18-year-old the No.10 shirt at the club - a squad number that will be available when Arjen Robben moves on in the summer.
Hudson-Odoi has played seven times this season and has 18 months left on his contract.
"What I can say: We like the player and take a great interest in signing him".
Bayern Munich have made no secret of their desire to sign Hudson-Odoi, with sporting director Sporting director Hasan Salihamidzic confirming on Wednesday that the club are working on a deal.
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And Salihamidzic has confirmed that the club are keen on signing the winger, telling reporters at Bayern's winter training camp in Doha: "He's a very interesting player that we really want to sign".
'Today it created a lot of confusion, I don't know what they have to do, but they have to explain it properly to the linesmen and referee to us, because if the guy stopped then I don't know why play kept going'.
'It was a general question from him.
Hudson-Odoi was in Chelsea's starting line-up against Tottenham on Tuesday night but has made the majority of his appearances for the club in the Europa League. I can advise him, but at the end of the day he decides about his future. You can see it from both sides.
'The referee told me they have explained it to us already but maybe they haven't explained it to the linesman because he stopped and if there is any doubt that it is offside he has to continue running. For his future, I wish him all the best.
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