The Spanish midfielder has made just two appearances for the Reds since joining from Bayern Munich this past summer.
Speaking on Thiago's knee injury, Klopp said: "On that day when he got injured in that bad challenge in the Everton game, there was another bad injury and after the scan there was good news and really bad news.
"[With Thiago] nothing was broken or ruptured but it was still a massive impact on the knee.
"The impact on the leg was that big that it's still not okay. It is not massive, and he trains from time to time, not at the moment because we have to realise we have to go through further steps."