New Blues boss Frank Lampard has insisted that Hudson-Odoi should stay at Stamford Bridge and wants to make him into a "world class" player.
The Sun says the player will happily put pen to paper on a five-year deal if given assurances over playing time.
That is the pitch of Bayern chairman Karl-Heinz Rummenigge, who is now trying to fill the gaps left behind by Franck Ribery and Arjen Robben.
Their first choice, however, is Sane.
A serious move for the Manchester City winger, valued at £90m, is set to commence this week.
"He wanted to think about his future. He certainly has.
"Now we have to wait and see if something is moving in our direction.
"It is no secret that we are still looking for a player for the wide areas. We are on the ball."