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The 22-year-old left-back is expected to leave Anfield on loan when the window opens, as he seeks regular first-team football.
TeamTalk reports Celtic have Chambers on their radar and see the former Kilmarnock loanee as a possible longer-term option.
A permanent transfer could also be considered because his Liverpool contract expires next summer.
Chambers has Scottish football experience from his Kilmarnock spell. He spent time on loan at Charlton Athletic and Wigan Athletic during spells away from Liverpool.
First-team chances at Anfield have been limited this season, making a January departure more likely.