The Reds centre-back will face a lengthy spell on the sidelines if it is confirmed that he sustained medial ligament damage in Sunday's match against the Red Devils
Agger was injured in a clash with team-mate Glen Johnson and stretchered off after the right-back subsequently conceded a penalty that Robin van Persie converted to seal three points for the visitors.
After the game Rodgers revealed that the Liverpool physios suspected that the 27-year-old had suffered damage to the knee and did not sound hopeful about his prospects of a quick return to action.
"Daniel Agger we'll need to wait and see," he told reporters. "It didn't look so good with his knee, and some of the medics were saying he may have a problem with his medial ligament, but we'll to assess that over the next 24 hours and look at it again tomorrow."
The duration of Agger's stay on the sidelines will depend on the extent of the damage done to the medial ligament. Johnson was coincidentally ruled out for three months of the 2009-10 season after suffering a tear to the same area.
The injury that ended Nemanja Vidic's 2011-12 season in December, meanwhile, was initially suspected to be a medial ligament problem but was later revealed to involve additional and more serious damage to his cruciate ligament.