The Welsh midfielder is struggling with a hamstring strain after recently recovering from a groin problem.
"We just need to see [with Allen]," Rodgers told the club's official website. "We've still got a wee bit of time to decide that, and he was on the training field today.
"It's just a case of assessing Joe on whether this game is going to push him too much and whether he's fully fit."
Liverpool head into the match in fourth place in the Premier League table, one point ahead of their Merseyside rivals.