Carragher will captain the Reds in their Europa League clash with Young Boys on Thursday evening, but the 39-year-old says it is hard to leave out the former England international in the club's bigger fixtures, given his commitment in training.
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"He works himself to a standstill every day of his life. And guys like that I want to put in the team when it matters.
"The Europa League matters of course, but every player wants to play in the Premier League on Sunday.
"And that is the most difficult decision I have as the manager of Liverpool - seeing him every day give his life to the club as hard as he does and then not being able to give him a shirt in the starting 11 at the weekend."
However, Rodgers insists that he will not force the 34-year-old to retire, and has offered him a role within the backroom staff at Anfield.
He added: "When I came in to 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. He's been a stalwart and has been a regular until the last season, so he was wondering where he goes.
"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.
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"His passions are for the football club, he wants what's best for the club and I enjoy working with guys like that.
"There's no doubt there's maybe that role beyond playing for him later on, 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.
"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."