The Liverpool forward suffered a hamstring injury on international duty earlier this month and was subsequently ruled out of action for a period of around six weeks.
Mane has been included in the Senegal squad for a World Cup qualifying double-header in November, leading to speculation that the 25-year-old could make an earlier return.
But, when asked for an update today, Klopp said: “Sadio is still in rehab, that’s how it is. He is indoor and was not even [doing] any exercises outside. That’s the situation in the moment.
“If he is fit earlier, I would be really happy but nobody knows in this moment. So, there’s nothing else to say about it.
“They have very important games or at least one; Senegal need one point from two games to be qualified for the World Cup, so I can imagine they feel the pressure a little bit.
“But we cannot change the situation. If Sadio is fit, we cannot hide it, why should we? If he is fit, we can do nothing to keep him here, he would go to the national team of Senegal, that’s clear. But in this moment, I don’t know.”