Alexander-Arnold did not make the trip to Portugal as Liverpool played their second match of this season’s Champions League campaign against Porto on Tuesday.
Klopp confirmed the right-back was absent due to an injury he suffered in Saturday’s 3-3 draw at Brentford, and said he may also be unavailable for selection for England’s upcoming internationals.
Speaking after Liverpool’s 5-1 victory over Porto, Klopp said: “Trent felt his abductor – in that area he has a little injury.
“No muscle injury heals that quick (in time for Sunday) – after that I don’t want to make the decision for him but I don’t think it will be possible for him to be with the national team. Hopefully after that he will be ready again.”
Prior to Liverpool’s win in Portugal, Klopp told BT Sport: “It didn’t look serious but we did further assessment and it was serious.
“He is out for today for sure, he didn’t travel, and it doesn’t look great for the City game as well.
“It’s a muscle thing. We thought it was just tight from the [Brentford] game but it was more and now we have to deal with that.”
Liverpool, the only Premier League club who remain unbeaten so far this season, welcome champions Manchester City to Anfield on Sunday.
Pep Guardiola’s City side moved to within a point of the Reds after beating Chelsea 1-0 at Stamford Bridge.