The vice-captain sustained a hamstring issue during the 1-1 draw at Brighton & Hove Albion on Saturday that forced him from the field and will rule him out of the Group D fixture.
However, Klopp reported more positive news with regards to Alexander-Arnold, Keita and Shaqiri, though they too are likely to sit out tomorrow’s Anfield tie.
“They are all getting closer to being back, [but] not close enough for tomorrow, I think,” said the boss.
“With Naby we have to check there still, but with the other two, they will not be ready.
“Trent looks quite good, but nobody gave me the green light for tonight so he will not be in it [training]. He hasn’t trained with the team and stuff like this.
“I saw him today on the pitch doing his rehab stuff outside, so that looks already good, but I cannot decide when this rehab stuff is finished. I take the players only in the moment when I get the green light and that didn't happen yet.
“But from my rather experienced eye from what I saw today, it will not be that long anymore with Trent.”