This is the third approach as the first began late in December and the Blues are now at a crossroads as they struggle to renew their talent’s contract.
Chelsea had offered Hudson-Odoi a five-year deal at the start of the season but he has been cautious about signing on after seeing how much game time he could get under Maurizio Sarri.
Former Napoli boss Sarri has struggled to find a place for the youngster in his line-up, using him in only six matches so far this season, and Bayern have proposed a development pathway where he could look to help replace ageing duo Arjen Robben and Franck Ribery.
Bayern's interest will remain beyond the summer, should they fail to land their man, but their offers are expected to drop in value as Hudson-Odoi enters the final year of his contract in June.
Sarri spoke about his difficulty in giving game time to the England Under-17 World Cup winner after his side’s recent win over Crystal Palace.
"I think that he is a very good player, the potential is there to become a great player, but now he has to improve,” he said at Selhurst Park. “With the ball, he is a very good player. He has to improve his movement without the ball.
“As a winger, he has to improve in the defensive phase, but he has the potential to become a very important player, not only for English football but for European football.
"I think [that he could play more] but it’s not easy. It’s not easy at this level to take the young players from the academy and he’s ready to play - not only here but everywhere in Europe.
"It’s not easy, and I think that we are lucky because we have [Ethan] Ampadu, we have [Andreas] Christensen, we have Odoi, so we are lucky. For players in the academy, we are really very lucky, or the academy is very good.
"In Europe there are few players with eight matches at this level [at 18 years old]. Odoi I think in this season played six, seven official matches in Europe, so I think that he has to be lucky. He is not lucky. He is good."
Bayern's move for the teenager comes hot on the heels of Chelsea announcing the £58m ($73m) arrival of Borussia Dortmund winger Christian Pulisic - a move that would likely see Hudson-Odoi move further down the pecking order.