The 29-year-old defender injured his ankle during the 1-0 victory over Manchester United at the beginning of the month.
"Glen is the type of player that you don't realise until he's not in the team, what you are missing," Rodgers said.
"He is athletic and he started the season very, very well. Against Manchester United he was outstanding.
"He's got the boot off his foot and he is working very hard. Hopefully in the next couple of weeks he will be back."
Good. It's a massive blow to us. He's one of the best around, and the difference he makes in the opposition half is priceless. It's a bigger blow than losing Coutinho because of the absence of anyone else who can do what he does from right back.- ajsr1982