The full-back has not travelled to Portugal with the rest of the squad for the Champions League group clash with Porto.
And Alexander-Arnold could now be ruled out of the Premier League showdown with rivals City on Sunday after Klopp’s latest update.
Speaking to BT Sport prior to Liverpool’s match with Porto, Klopp said: “Unfortunately Trent went in early [from training]. It didn’t look serious and in the end it was serious.
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“He’s out for today for sure, and he doesn’t look great for the City game as well.
“It’s a muscle thing. We thought he was just a bit tired from the [Brentford] game but it was more and now we have to deal with that.”
If the injury – believed to be a groin problem – is as bad as it sounds, it could well keep Alexander-Arnold out of the England squad over the international break, which begins after Sunday’s fixture at Anfield.
Liverpool are then next in action on October 16 when they travel to Watford.
James Milner has already deputised for Alexander-Arnold in the right-back slot against Crystal Palace this season and was selected to start vs Porto.
But Klopp will no doubt be frustrated to lose Alexander-Arnold ahead of such a crucial match, with Liverpool currently just a point ahead of City in the table.
Klopp revealed on Monday that Alexander-Arnold had taken the place of Georginio Wijnaldum in Liverpool’s ‘captain’s group’, with Andy Robertson and Alisson also added as the fifth and sixth members.
The Reds’ boss has been mixing up his selection this season to keep his players fresh, but admitted he and his staff did not feel it necessary for the challenge of Porto.
How should Klopp cover Alexander-Arnold’s injury vs Man City? Have your say below.
“It’s always a question of fresh legs or rhythm we decided this time for rhythm,” Klopp added. “Normally you have to rotate but in this situation we don’t have to the boys can go again.”
Liverpool top their group going into the fixture, while City face a difficult test in France as they meet Lionel Messi’s PSG.
The news regarding Alexander-Arnold’s injury comes on a sad day for the club as legendary striker Roger Hunt passed away aged 83.
Klopp paid his own tribute to Hunt and told BT Sport: “It’s difficult obviously. We don’t know these legends personally but the first thing you learn when you come to Liverpool is about these guys.
“He would have been a player that would have played definitely in my team. It is really sad. Condolences go to his family from the Liverpool family. It is a really sad day.”