Daniel Agger and Mamadou Sakho are also ruled out, but Rodgers told reporters ahead of the game: "We don't have a lot of choice at the moment. We've only got 15 players training [due to injuries], and obviously we'll call on some of our younger players to come into the squad.
"It's a competition we want to do well in, the history of the club dictates that it's about winning trophies and this game is important for us, so we'll be strong and look to get a good result.
"It's always been the priority, to arrive in there [the top four], but as I said this club is about trophies, and winning trophies. This game is one we'd like to win."
The Reds beat Oldham Athletic in the third round.