The 23-year-old has enjoyed an impressive campaign so far and provided 17 assists from the full-back position in all competitions.
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Speaking in a news conference on Friday ahead of Liverpool's FA Cup quarterfinal tie at Nottingham Forest (Stream LIVE on Sunday on ESPN+ in the U.S.), Klopp said he is unsure when the defender will return to action.
"Trent is out with a hamstring, so will be out for England too," he said. "Not good news, we will see how long it takes. We will see how it will take.
"To replace him is difficult but possible. We have [James] Milner, [Joe] Gomez, these kind of things. Trent is so influential but Milner has done incredibly well in the past. We'll see how Milly is for Sunday. Maybe a young solution?"
Alexander-Arnold was called up for England's upcoming friendlies but Gareth Southgate will need to find a replacement in defence.
Liverpool have already clinched the Carabao Cup this season and Klopp said he wants the opportunity to return to Wembley for the FA Cup semifinals and final.
"It was a while ago we played a final at Wembley [before the Carabao Cup final]," he added. "The atmosphere the people created, no difference to the Champions League final.
"This is a fantastic opportunity. Nice to play semis at Wembley but the real deal is a few weeks later."