Sky Deutschland says Bayern made another move last summer but couldn't lure him away from Stamford Bridge and Hudson-Odoi eventually committed his future to the club, signing a huge new contract worth around £50m over five years.
But Bayern have not been deterred in their pursuit and are set to make another offer for the winger.
It is claimed there has already been contact from the recently-crowned Champions League winners to Hudson-Odoi's representatives.
They have not yet made official contact with Chelsea but would be interested in an initial loan move with an option to buy.
It is also reported that Juventus and RB Leipzig are keeping tabs on Hudson-Odoi.