Senegal winger Mane may be fit enough to return to the bench after a month out, but Philippe Coutinho (adductor) 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 yesterday for the first time with the team and looked really, really good. We will see what we do with that," Klopp told a news conference.
"Yesterday it looked like he is ready for at least 20-25 minutes but we have to wait to see how his body reacts to the session because for him it was pretty intense; not because it was intense but because it was his first football session for a long time.
"He did really well, he obviously didn't miss his abilities or skills during the injury break, so that’s good."
Previously, 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.
"Things are like they are, we cannot change that. We cannot sit here and ignore the situation of Senegal and say we don't care if they play in the World Cup – that's not nice and it's not right.
"We will get into contact with Senegal FA and they have two games to play. Sadio is not injured anymore. Is he 100 per cent fit? That's different, but he is on a good way and yesterday he looked really good. We will have to see what we do. If you see Sadio training, you are like, 'OK…maybe we can use him!' and maybe that's the same for Senegal."
While Mane is set to return for Liverpool, Klopp also addressed other fitness issues at the club, including confirming Coutinho is out for this week, while Georginio Wijnaldum and Dejan Lovren's statuses are up in the air.
"Phil is not available. With the rest, it will be close. Gini I'm not sure, we have to see. It's painful what he has but maybe he can cope with it. We will have to see," Klopp said.
"Dejan, yes, maybe today is the clearing session and we know that in weeks like this you have to wait until the last second to make the squad or the line-up."
Meanwhile, the manager also provided updates on Adam Lallana and Nathaniel Clyne who have been both been sidelined long-term with injuries.
"Adam is close but didn’t train so far with the team. He will start next week so that’s good, and then hopefully he can have two proper training weeks and then he will be available.
"(Clyne's status is) not that good. He was on a good way and then he had a little setback but we are on it. That’s how back problems are.