The summer signing from Bayern Munich has been sidelined since October with a knee injury but is closing in on a return.
"He is eager [to get his Liverpool career up and running]. We are already making jokes here that we should sign Thiago for January," said Klopp.
"He gets closer and closer but we will not rush it.
"But it's nice to have him on the pitch doing a lot of stuff. He's not in team training yet and that's the final step.
"We will see how he looks on the pitch over the weekend. Will he be back in team training next week? He has to have a few tests before he can be back.