The Spain international has not featured for the Reds since the 2-2 draw in the Merseyside derby at Goodison Park on 18 October (AEDT).
Thiago has only played twice for Liverpool since arriving from Bayern Munich in a deal that could reportedly cost up to £25million.
Still, his performances against Everton and Chelsea highlight the impact of his absence. Thiago has attempted (107) and completed (98) more passes per 90 minutes than any other Liverpool midfielder this season.
Significantly, the former Barcelona man attempted 21 passes into the attacking third on average in those two games, at least eight more than any other Reds midfielder in 2020-21.
Liverpool enjoyed a five-game winning streak in all competitions after the draw with the Toffees, but Klopp's side have since won only once in four matches, a run that includes a 2-0 home defeat to Atalanta in their previous Champions League match.
They therefore head into Tuesday's game with Ajax knowing they require a draw to guarantee their place in the last 16 before matchday six.
While captain Jordan Henderson is fit to start, James Milner (hamstring) is set to miss out and Thiago will certainly not be involved.
"Thiago we have to maybe clarify it a little bit," Klopp told reporters on Monday.
"On that day when Thiago got injured in that challenge in the Everton game, there was another bad injury [to Virgil van Dijk] and after the scans it was like one was really bad news and the other one was really good news because nothing was broken, nothing was ruptured and stuff like this.
"But, as we realise now, it was still a massive impact on the knee. The problem is in a situation like that, nothing is ruptured and nothing is broken and that means everybody thinks, 'Okay, you can go after a few days', but the impact on the leg was that big that it is still not okay.
"It is not massive and he trains from time to time, not in the moment because we just have to realise that we have to go a few further steps. I can't say exactly when he will be fine, but it will take a few weeks still with Thiago."
Klopp was involved in a heated exchange with BT Sport reporter Des Kelly after Saturday's 1-1 draw with Brighton and Hove Albion, offering the broadcaster "congratulations" after Milner's injury.
The Liverpool boss has spoken often of the risk to players' welfare during the packed 2020-21 schedule, which has seen his side play three times in seven days since the international break.
Speaking to UEFA.com, Klopp reiterated his concern about the mental and physical state of players attempting to be at their best every three days.
"For the players, it's incredibly intense what we are doing," he said. "We're all happy and it's without any alternative that we play. It's great – love it, fantastic – but it's all on the backs of the players.
"They have to deliver. You watch the game and if they don't play well, you still think: 'That's not really good!' You don't think about what they go through in the week, because we all have normal lives, obviously, left and right of the games we play.
"And that's pretty much the same for all of us, where you cannot see friends, you cannot see your family, and all these things. Recovery is not only sleep, it's not only treatment. It's really giving yourself a bit of freedom to think about things you want to think about and not what you have to think about.
"In the world out there at the moment, the biggest problem is that we don't have this time often enough and it keeps us quite tense. That doesn't help if then you have a game to play every three days at 110 per cent, in the best way."