The 20-year-old was injured in the warm-up before the clash with Brighton & Hove Albion on Saturday. After playing the full 90 minutes of that game, BBC Sport's Phil McNulty suggests he will now miss a minimum of two weeks with the problem.
The Guardian's Andy Hunter claims that absence could easily reach up to a month after tests revealed a minor ligament issue for the English international.
That timeframe seems certain to encompass the home games against Crystal Palace and Leicester City and a visit to West Ham United. It could also threaten his availability for the Champions League last-16 first leg against Bayern Munich on Feb. 19.
This could present a serious problem for Jurgen Klopp. Alexander-Arnold has missed just two Premier Lague games all season and has established himself as a consistent performer for the title-chasing team.
From once being flush with right-backs, the Reds are now short in the position after backup Nathaniel Clyne joined Bournemouth on loan earlier in January.
The Reds host Palace on Saturday.