Mane was taken off with a minute remaining in Senegal's 2-0 World Cup qualifying win over Cape Verde Islands on Saturday.
Strikers Daniel Sturridge and Dominic Solanke will also vie for a starting berth in Mane's absence, while Klopp may instead choose to deploy Philippe Coutinho higher up the pitch alongside Roberto Firmino and Mohamed Salah in attack against United at Anfield.
Liverpool's hopes of gaining ground in the Premier League title race have suffered a major blow after forward Sadio Mane was ruled out for up to six weeks with a hamstring injury.
Mane will miss the visit of United on Saturday as the Premier League returns following the global break, plus a number of other potentially crucial encounters, including the trip to Tottenham on October 22.
Mane has endured a tough start to the season, having already been suspended for three domestic games after being sent off for a high foot versus Manchester City.