The 18-year-old is keen on moving to the Allianz Arena but Bayern have seen three bids rejected for the winger.
Bayern announced the signing of 2018 FIFA World Cup victor Benjamin Pavard from Stuttgart for the 2018/2019 campaign, but they now have their sights on the Blues' highly-rated Callum Hudson-Odoi.
Hudson-Odoi decided he wanted to leave Chelsea in the summer after growing exhausted of failed promises for game time, much like Paul Pogba did at Manchester United during his first spell at the club.
The 25-year-old, who made 66 Bundesliga appearances with Stuttgart, claims that he has been offering advice to Hudson-Odoi about what life's like in Germany.
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'What I can say: We like the player and take a great interest in signing him. "It was just a general question from him to know, because he is still young".
He then started and impressed again in Chelsea loss to Tottenham in the semi-final, first leg of the Carabao Cup on Tuesday night. He is still young, I can advise him, but at the end of the day, he decides about his future. Of course, he can develop in Germany as well and don't forget Bayern Munich is also a big club.
'All credit to him, he has shown what he is capable of, shown why he is getting this attention and hopefully he signs his contract and does it many more times for Chelsea'.
They have seen him break into the first-team fold at Stamford Bridge this season, but feel more opportunities can be presented to him in Germany.
Bayern are said to be ready to pay upwards of £35 million to bring the player to Germany.