Alexander-Arnold, 21, encountered the issue during the Reds’ last match before the international break which meant the West Derby full-back remained on Merseyside as opposed to linking up with the England squad.
According to The ECHO, he will step up his rehabilitation at Liverpool’s brand new AXA Training Centre next week as he sets his sights on a swift return to action.
However, Alexander-Arnold awaits a race against time if he is to declare his fitness ahead of Liverpool’s final Champions League Group Stage match in Denmark against FC Midtjylland on December 9.
It means Jurgen Klopp and Liverpool are expected to be without the services of the 2020 PFA Young Player of the Year for league matches with Leicester, Brighton as well as Wolverhampton Wanderers.
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Liverpool will also be without both Jordan Henderson and Mohamed Salah when the Reds welcome Brendan Rodgers back to Anfield on Sunday.
Henderson, 30, is expected to miss the encounter following a groin injury he sustained while on national team duty with England.
The Liverpool club-captain was removed at half-time during the 2-0 defeat to Belgium on Sunday and was subsequently sent back to Merseyside to to await further assessment.
Meanwhile, Liverpool will also be without top-scorer Salah after the Egyptian international tested positive for COVID-19 again on Wednesday.
Salah could also miss Liverpool’s Champions League clash with Atalanta next Wednesday as well as the trip to Brighton on November 28.