Hudson-Odoi is still keen to leave Stamford Bridge after Bayern Munich attempted to sign him in January.
The Bavarians maintain an interest and are expected to go back in for the 18-year-old at the end of the season.
But, according to German outlet Kicker, they will face competition from the Reds who have already made contact.
The Blues are reluctant to lose the 18-year-old as they face a two-window transfer ban imposed by FIFA for irregularities in the market.
Chelsea knocked back bids from Bayern in January, the most recent of which was £35million.
Despite his undoubted potential, recently rewarded with a call-up to the full England squad and a subsequent international debut, he has struggled for a starting spot under Maurizio Sarri.