Mane could return for Liverpool at West Ham
Senegal winger Mane may be fit enough to return to the bench after a month out, but Philippe Coutinho (back) will not make the game at London Stadium.
A hamstring injury has kept Mane out of action since the last international break, and was initially expected to keep him on the sidelines until after the upcoming pause for national action.
However, a return to training on Thursday could be followed by a comeback to the pitch.
"Sadio trained with the team for the first time yesterday and looked really good," Klopp told a news conference on Friday. "We will see how he reacts. He could be ready for 20-25 minutes.
"Coutinho not available. With the rest it will be close, [Georginio] Wijnaldum, I'm not sure. It's painful."
"Sadio trained yesterday and looked really, really good."
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Senegal coach Aliou Cisse claiming last month that Mane would be "100 per cent fit" for their World Cup qualifiers against South Africa had baffled Klopp.
But the German dismissed any notion that he would try to block the winger's call-up, with Senegal needing a win from two games to seal a place at Russia 2018.
"We cannot ignore Senegal, that's not fair," Klopp said. "FIFA doesn't give you the opportunity to decide who plays for countries. We respect the rules.
"Training is different and I would love to have more influence."