Carragher will captain the side in Thursday night's UEFA Europa League clash with Young Boys, and the boss insists he remains an important part of his future plans.
"When I came into the club I had a real good chat with Jamie and he wasn't sure himself where he was at in terms of his career and where he was going," said Rodgers.
"He's been a stalwart and a regular until last season so he was wondering where he goes.
"I've been so impressed by Carra on and off the field. He's an incredible character and I can see why he has played more than 700 games for this club because his focus and concentration into his work is phenomenal.
"I think he can play on. He's one of the guys who's the soul of the club and there has to be a place for someone like him. Whether he wants to do that is another thing.
"I arrived into here and heard these stories about him kicking the ball long up the pitch, but this is one of the best technical players we have — left foot, right foot, touch on the ball, reading of the game, tactical intelligence, he has it all.
"Okay, the legs may not be the same as they were six or seven years ago, but he still has a lot to contribute for me. His passions are for the football club, he wants what's best for the club and I enjoy working with guys like that. He's a great role model for everyone here.
"There's no doubt there's maybe a role beyond playing for him here, but for me, what he has given me in these opening few months there is no reason he can't play on for a few more years yet."
For the Barclays Premier League games so far, Rodgers has paired Daniel Agger with Martin Skrtel at the centre of his defence, and he admits leaving out Carragher is one of the toughest decisions he faces.
"For me, it's the hardest part of my job because every day of his life he comes in and he gives his all," Rodgers added.
"Every day he gives 150 percent commitment, he works to a standstill every day of his life. Guys like that I want to put in the team when it matters. The game against Young Boys matters of course, but every player wants to play in the Premier League on Sunday.
"That is the most difficult decision I have as the manager of Liverpool, seeing him every day give his life to the club and then not being able to give him a shirt in the starting 11 at the weekend.
"But saying all that the incredible humility he has got, the type of man he is, he makes it as easy as possible for me — he gets on with his work."
Meanwhile, Moroccan international Oussama Assaidi is expected to make his Liverpool debut in Switzerland and Rodgers insists he has settled in well.
"Assaidi has had a few weeks to adapt and now he's ready to play," he added.
"It was difficult for him because he was injured for a bit and then he wasn't eligible for the games against Hearts. But he has settled in well and this will be his first opportunity.
"He's an exciting player — someone who can take people on. He gets crosses in and has got an end product.
"That's important because I like players at the top end of the field who have that invention, fight and ability to score goals.
"He's good on one v ones and is a technical player who is strong and uses his body well.
"I'm looking forward to seeing him play against Young Boys and seeing how he adapts to playing in this team."
The boss also confirmed Brad Jones will start in goal in place of the rested Pepe Reina.
"Brad will play and he deserves it," Rodgers said. "He has been first class. He's not had a look in but he's come in every day and worked well."
Photo via Liverpoolfc.com