The Denmark international limped off towards the end of Sunday's 2-0 FA Cup victory over Oldham, leaving the Reds playing with 10 men as they had already used all three substitutes.
After the match manager Brendan Rodgers said Agger had felt cramp in his calf but the player's reaction to the injury, immediately signalling to the bench he could not continue, suggested it could be more serious.
Agger had a scan on the affected area on Tuesday and Rodgers is due to meet with the club's medical staff to assess the results.
Liverpool are already without defenders Mamadou Sakho (hamstring) and Jose Enrique, who is still recovering from a knee operation, while full-back Glen Johnson sat out the Oldham game after jarring his ankle against Hull on New Year's Day.
Wednesday also brings a 6pm deadline for Rodgers to respond to a Football Association charge for allegedly questioning the integrity of referee Lee Mason.
His post-match comments following the Boxing Day defeat at Manchester City appeared to question whether it was correct to have an official from Greater Manchester in charge of the game.
"I was surprised we are playing in Manchester and have a referee from Greater Manchester. I am sure we won't get (for) Liverpool-Man City someone from the Wirral," Rodgers said at the time.
The day after the game Rodgers insisted he was trying to make a valid point, saying: "In terms of geography, I certainly wasn't questioning the integrity of referees. I think the FA and the Referees' Association know perfectly well I am someone who engages in supporting the referees."
However, the FA subsequently charged Rodgers after alleging he had "called into question the integrity of the match referee, and/or implied that the match referee was motivated by bias; and/or brought the game into disrepute; and/or amounted to a failure to act in the best interests of the game".