The Dane was injured after he clashed with team-mate Glen Johnson, moments before the right-back conceded the penalty from which Robin van Persie netted the winning goal in an intense match with Sir Alex Ferguson's men.
The centre-back was stretchered off the field after a prolonged stoppage before the Dutchman's spot-kick, with Reds' boss Brendan Rodgers admitting after the game that he feared the 27-year-old had done medial ligament damage.
|11/1||Liverpool are 11/1 with Bet365 to beat WBA 2-0 in the League Cup
However, despite initial reports suggesting the player could be out for the rest of the season, it now appears that the Denmark international will be back in training in a couple of weeks after it emerged he did not tear any ligaments.
Per Steffensen, Agger's representative, told jp.dk: "There is good news. He has not torn ligaments. He has a small rupture behind the knee and it has swollen and sore but once the swelling goes down he can train again."
Following the news that the Liverpool man did not suffer a tear he should be back in training in one or two weeks, however team-mate Martin Kelly has not been as fortunate after he tweeted that he will not return until the new year.
Rodgers' side face a trip to West Brom in the League Cup on September 26 in their next outing, which may be a welcome break from the Premier League, where they are still winless, after the 2-1 loss to Manchester United at Anfield.
However, the Merseyside outfit will go into the clash with bad memories of the Hawthorns, after they lost 3-0 there on the opening day of the season.