According to Bild, the Reds are keeping a close eye on the 18 year-old, further muddying the waters of the England prospect's future after the Blues refused to allow him to talk to Bayern in January.
The Bundesliga champions had a £35million rejected during the winter transfer window, with Chelsea stressing they are not ready to allow the academy graduate to leave this early in his development.
Hudson-Odoi has not started a Premier League game for Chelsea this season, and has been limited to appearances in the FA Cup and Europa League where he has impressed with a clutch of goals and assists.