Mane returned from Senegal duty with bruised ribs, while Henderson sustained a minor injury in England's World Cup qualifier against Albania last week.
Right-back Robertson was also forced off in Scotland's 2-0 win over Denmark on Monday, which guaranteed the Scots' spot in the 2022 World Cup play-offs as a seeded team.
The injury news during the international break led to fears from Liverpool supporters ahead of their Premier League clash against Arsenal this weekend - which is LIVE and EXCLUSIVE on talkSPORT.
"Robbo was lucky, we can probably say," Klopp told Liverpool's website.
"It was a little bit DOMS [delayed onset muscle soreness], the intensity of all the games he played probably, rather than anything else.
"He was smart enough to [make] the right decision, he went off early, which he usually is not doing but in this case it was absolutely right, and so there's a good chance that he can be involved at the weekend.
"Hendo, a little bit more [injured] than Robbo, but a chance for the weekend so we are working on that.
"It's not a serious injury but in this short period of time we have to see if he is ready for Saturday, but after that, 100 per cent, and possibly for Arsenal as well."
Mane has been passed fit but fellow forward Divock Origi will be assessed after sustaining a dead leg playing for Belgium.
"Sadio is fine - painful but fine," added Klopp.
"Everybody who had a rib bruise knows it's an annoying thing. But Sadio trained here with us now in all sessions."
Midfielders Naby Keita and James Milner [both hamstring] will not be ready for the weekend but could potentially feature in the Champions League at home to Porto on Wednesday.
"Naby and James are in a good way as well, getting closer," said the Reds boss.
"Probably next week we expect them being back in team training, let's see what that means for the Porto game - but not for the weekend, they are not available."
Defender Joe Gomez [calf], forward Roberto Firmino [hamstring] and midfielder Curtis Jones [eye] remain sidelined for longer.