The Merseysiders sit 16 points clear at the English top-flight summit and will catch up their game in hand when they travel to London Stadium in midweek.
Mane came off after 33 minutes in Thursday's 2-1 win at Wolverhampton Wanderers due to the injury.
Klopp has been critical of England's congested winter schedule and again appeared dissatisfied with the amount of games played in his update:
"Sadio will not be involved for West Ham and probably not for Southampton. After that he should be then fine. The week we have then after that is for him perfect to get back on track.
"He has a small muscle tear, which is serious enough to keep him out. We were lucky with the injury as well, so it was not that serious.
"But of course, when you have three games in a week then that means he is out for these three games."
Liverpool will move 19 points clear of Manchester City provided they win, while West Ham will move into the relegation zone if they lose by more than three goals.
There are 44 points separating Wednesday's opponents ahead of kick-off, but former Everton chief David Moyes—now at the West Ham helm—would relish a result against the rampant Reds.
Klopp's side were held to a 1-1 draw the last time they travelled to London Stadium in February 2019, when Mane opened the scoring before Michail Antonio's equalising effort:
It seems unlikely Klopp will risk the Senegalese star's fitness for the home meeting with Southampton, despite the Saints having won five of their last seven Premier League games (one defeat).
The manager's outlook could change should West Ham snatch a result before then, though that seems unlikely considering the Hammers are without a win in four ahead of the home clash.
January signing Takumi Minamino replaced Mane at Molineux and looks a natural fit to make his first Premier League start on the left flank against West Ham.