By ESPNSTAR.com staff
The 34-year-old's only Barclays Premier League appearance this season came as a second-half substitute in the 3-0 opening-day defeat at West Brom.
However, Carragher has started three of Liverpool's four Europa League games this season and is set to captain a second-string Reds side on Thursday night in the competition for their Group A match against Young Boys in Berne.
Carragher is considering retirement at the end of the season and Rodgers has revealed that he would be happy to retain at the club the veteran as a coach or a player.
"I had a conversation with Jamie when I first came in and he wasn't sure about where he was at in his career," Rodgers told the Guardian.
"He has been a stalwart at this club and was a regular until last season. But I've been so impressed by him on and off the pitch.
"I think he can play on. He is one of the guys who is the soul of this club and there has to be a place for someone like him. Whether he wants to play on is up to him.
"He is one of the best technical players we have here - left foot, right, his touch and his reading of the game. Okay, the legs might not be what they were six or seven years ago, but he's still got a lot to contribute.
"No doubt there is a role for him later on but there is no reason why he cannot play on from what I've seen over the last few months."
Carragher's recall into the first XI for the game against Young Boys comes about as Rodgers looks to rest his key central defensive pairing of Martin Skrtel and Daniel Agger for Sunday's league clash against Manchester United.
Rodgers admits that Carragher's commitment to Liverpool has not made it easy for him to leave the defender out of his starting line-up in the Premier League.
"He is the hardest part of my job," Rodgers said.
"Every day of his life he comes in and gives his all.
"Guys like that you want to put in the team when it matters. This game matters, but all players want to play in the Premier League, and not picking him is the most difficult part of my job as Liverpool manager.
"Seeing him work so hard and not giving him a shirt is the most difficult job I've got."
Captain Steven Gerrard, Luis Suarez, Jose Reina, Glen Johnson, Joe Allen and Martin Kelly have also been left behind for Thursday's Europa League clash with Swiss side Young Boys.