But he is hopeful that the Spaniard and Stefan Bajcetic, who has also been dealt a further injury blow after his recent comeback, will be available again after the international break.
Thiago has not featured for Liverpool since going under the knife in May, with attempts to resume full training now twice thwarted by fresh fitness blows.
Bajcetic, meanwhile, featured in wins over LASK and Leicester after overcoming an adductor injury, before being condemned to the sidelines once again.
“Not massive but enough to take him off the pitch again. Obviously not the same injury, not at all, but a bit similar.
“And as annoying as it is for Stefan Bajcetic. Was there, played a few minutes, and then felt something else. That’s how it is after long-term injuries from time-to-time.
“I don’t know, I will not put pressure on [when they can return]. If they will be back after international break, we will see. Hopefully, would be cool.”
The Dutchman is already closing in on a return to action, and is likely to be joined by Conor Bradley, who has been out since suffering an injury in pre-season.
Klopp added: “Cody has a good chance that he will be back [after the break]. Already out of the brace, walks normal around here.
“So from all the very, very bad opportunities and possibilities injury-wise, we nearly got the best, but he is still injured.
“And Conor is on the way back. He is running. In that age group and with these kind of injuries, you tend to give them rather three weeks more than not enough because it has to be better.
“It has to do with the growing process of the body. Stuff like this.
“I couldn’t get this injury anymore, let me say it like that. And that’s why they need a bit of time.”