The 18-year-old is expected to return from an achilles injury in four to five months.
He will be free to speak with any foreign club in January when his Chelsea contract enters its final six months.
The Sun claim Bayern have not forgotten about Hudson-Odoi since their failed attempts to sign him last January.
The report claims the England international is desperate for a move to Allianz Arena after suffering with inconsistent playing time under Maurizio Sarri this season.
Chelsea will be hoping they can use his recovery period to sway the academy product to remain in west London.