Mane suffered a hamstring injury while on duty for Senegal in the international break and is expected to be out for around six weeks in what is a blow to Klopp in the build-up to Saturday's lunchtime clash earlier this week.
However, the rest of the Reds' international contingent have returned without any issues, with both Philippe Coutinho and Roberto Firmino fine to train on Thursday and Friday despite being involved for Brazil.
Adam Lallana and Nathaniel Clyne are recovering well from their injuries but the United clash comes too soon for them. Andy Robertson will hope to be involved after starting just two Premier League games so far following his summer move from Hull City.
Klopp is well aware just how big the game is and he knows United boss Jose Mourinho will adapt his tactics for the trip to Anfield.
He told reporters: "It's a massive game. I would have liked more time to prepare for the game, both teams have had exactly two days to prepare.
"Sometimes (United) defend pretty deep and sometimes they have a high pressure, against us (last season) they played long at times but they don't do that all the time.
"They have big quality but we are still positive when we think about the game and we're really looking forward to it as it's one of the most special games in world football. We want to perform and get a result."