The defender sustained an injury during the match at Manchester City on Sunday.
TAA was forced from the field after 63 minutes at Etihad Stadium after pulling up with an issue during the 1-1 draw in the Premier League.
According Klopp, Alexander-Arnold will be ruled out of England’s fixtures with Republic of Ireland, Belgium and Iceland during the international break, with the Reds awaiting further diagnosis following a scan on Monday.
Klopp in post-match press conference said "Trent will be out for England, that is clear.
“What he has, we don’t know, but he cannot play for England.
"He will not be the last and not the only one who Gareth [Southgate] will miss for this international break.
"He will have a scan tomorrow and then we will see."
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