The Reds initially put a six-week timeframe on Mane's recovery, ruling him out until late November, but Senegal coach Aliou Cisse has included the attacker in his squad to face South Africa on November 10 and 14.
Cisse claimed Mane would be "100 per cent fit" to play as Senegal look to tie up a place at the World Cup, but Klopp has a different view.
"I don't know how he [Cisse] can know – I don't know, that's how it is," Klopp said.
"Sadio is still in rehab, it is indoor, not even for any exercise outside, that's the situation at the moment. If he is fit earlier I would be really happy but nobody knows, so there is nothing else to say.
"They have very important games don't they, so that's to be qualified for the World Cup I imagine they feel the pressure a little bit, we cannot change the situation.
"If Sadio is fit, we cannot hide it, why would we? If he is fit we can do nothing to keep him here and he will go with Senegal."
Senegal is on top of CAF Group D by two points over second-place Burkina Faso with a game in hand.