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Mamadou Sakho could miss the start of the season because of an Achilles injury.
Sakho had been free to return to Klopp's first-team after being cleared of a doping charge by UEFA, which resulted in him missing the Europa League final and Euro 2016, but the French defender is facing a spell out of the game through injury.
The 26-year-old has yet to recover from the Achilles injury that troubled him towards the end of last season and manager Jurgen Klopp admits it could be another month before he is ready to return to training.
"Mama had a little issue with his Achilles when he was playing [last season], one day on, one off, this kind of thing," Klopp told reporters.
"When he had his little 'break' he used the time to have a little bit of treatment and that now means another three or four weeks before he can train again.
"There was no surgery, he is just not about to train at the moment. He has got some rehab of course and it's not too good a situation for him, for us, everybody.
"It's not important what I could say because everyone thinks the same. He's here, he's not available at the moment but he is doing rehab. We will see how he reacts to that and then when he can play again."
Sakho was initially banned for 30 days after he tested positive for a banned fat-burning substance after the Europa League tie against Manchester United back in March.
The suspension saw him miss out on a place in France's Euro 2016 squad and the defender is considering taking legal action.
"I cannot say too much as a manager. I don't know exactly what will happen now from Mama's side or UEFA's side," Klopp added.
"But as a human being I can say it's a sad story. He didn't play now for three-and-a-half months. That's obviously not really cool but we all know that doping is a very serious thing and we cannot have that.
"But I am sure they tried to do the right thing. Others have to talk about this because I don't know what I am allowed or able to say. That's one thing and the other is that Mama is currently injured."