Lovren was not involved as Liverpool stormed to a 4-0 victory over West Ham on Sunday, having been unable to train due to an injury sustained towards the end of last season that was made worse during Croatia's run to the World Cup final - the former Southampton man having played a crucial role in that campaign.
And Klopp has now put a timeframe on the 29-year-old's return, expecting Lovren to rejoin the squad for training inside three weeks.
"He is not fit. Let me say it like this, last year he already had a few problems with that but he could obviously play - and played really good," Klopp told Liverpool's official website.
"Recovery days were always enough then it was not a problem and he was in the next session again. We did not train a lot in the end of the season, of course, because we were more or less constantly playing, but he played constantly.
"Now in the World Cup, [playing] three times [for] 120 minutes it got a bit worse, but I am pretty sure it will settle in the next one, two or three weeks.
"In that time he can probably for sure train already, but not the full programme, so that will then take time.
"In the end, it is serious but not that serious. In the moment he is not available, that's true."