The 25-year-old right-back suffered a recurrence of a knee problem in the first half of Liverpool's 3-1 home win over Burnley last weekend and was subsequently withdrawn at half time.
Manager Jurgen Klopp confirmed after the match that Alexander-Arnold's fresh injury would be assessed to determine the severity of the issue, with initial reports suggesting that he could be sidelined for two months.
According to The Telegraph, the timescale is unspecified, but Liverpool's encounter with Chelsea in the EFL Cup final at Wembley Stadium will come too soon for Alexander-Arnold.
The report adds that the England international is optimistic that he will recover in time for the Reds' Premier League clash with Nottingham Forest on March 2, eight days before a title showdown with champions Manchester City at Anfield.
Alexander-Arnold is expected to miss Liverpool's next two Premier League games, before the EFL Cup final, at home against Brentford on Saturday and versus Luton Town four days later.
It remains to be seen whether the versatile defender could be fit to return against Southampton in the FA Cup fifth round, a fixture that Klopp will be keen for Alexander-Arnold to feature in to build up his match fitness ahead of the crucial visit of Man City on March 10.
Alexander-Arnold was sidelined for three weeks with a knee injury earlier this year and subsequently missed three games in all competitions, including both legs of Liverpool's EFL Cup semi-final clash with Fulham.
The defender's latest setback comes as a huge blow for Liverpool and their hopes of lifting their first piece
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