The Reds' vice-captain came off in the 71st minute of his side's 3-0 win over Aston Villa a fortnight ago and was forced to withdraw from the England squad for the recent international break.
Alexander-Arnold was nowhere to be seen in training on Thursday morning either, sparking concern about his availability for the lunchtime trip to Molineux.
Klopp confirmed the worst when addressing the media in his pre-match press conference on Friday, although he affirmed that Alexander-Arnold had avoided a serious injury and should be working with the ball at his feet again next week.
"[There is] no concern. He is not available, we knew that before. He didn't train with the team once yet and will take a little bit," Klopp told reporters when asked about Alexander-Arnold's fitness.
«It is not the worst hamstring injury you can have but it's a hamstring injury and they barely heal in two weeks -and this one didn't, either. As he is running already, we hope he can start ball work early next week and then we will see and go from there.»
Klopp will therefore be without both his captain and vice-captain for Saturday's early kickoff, as Virgil van Dijk has been banned for an extra match for admitting to using insulting and abusive language at Newcastle United last month.
However, Klopp had more reassuring updates to share on Ibrahima Konate and Darwin Nunez, the former of whom has also missed Liverpool's last two games with a thigh problem and could not turn out for France over the past two weeks.
Konate was pictured in training on Thursday, although the same could not
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