Earlier this month, the winger was ruled out for six weeks after picking up the problem while on international duty with Senegal, but the 25-year-old has already been selected for his nation's World Cup qualifiers next month.
However, while Klopp has left the door open for Mane to feature for his country, the German has revealed that the player is not close to a return to training.
The 50-year-old told reporters: "Sadio is still in rehab. He is indoors. He is not in any exercises outside. I can imagine [Senegal] feel the pressure a little bit.
"If he is fit earlier I would be really happy. But nobody knows at this moment. If he's fit, we cannot hide him. we can do nothing to keep him."
Mane has contributed three goals and one assist in seven appearances this season.