The Reds boss says that he is hopeful the veteran will take up a coaching position at the club after he retires from playing at the end of the current season.
The 35-year-old Carragher confirmed earlier this month that he will bring his playing career to an end when his contract expires, and ex-Liverpool stars Ian Rush and Steve Nicol have both called on the club to offer a coaching role to the defender, who is also considering a career as a media pundit.
Rodgers expects Carragher to take some time away from the game after his retirement, but he hopes that he is eventually able to bring him back to Liverpool.
"I've had regular conversations with Jamie since I came in last summer," Rodgers told TalkSPORT. "He's a guy who's put his heart, soul, and life into Liverpool. As one of the local players, there's even more pressure on him.
"He's been outstanding this season, even when he hasn't been playing. As a manager it's a real privilege to work with someone like that because he's very committed, has got old-school values and ethics, and really respects me and my decisions.
"He works very hard to prove that he's still good enough to be in the team. Even at 35, he's still one of the best pure defenders in the Premier League.
"He hasn't totally made up his mind what he's doing yet. It wouldn't surprise me if he had a small amount of time away but, over time, I'm sure he'll have a role here at the football club.
"But at the moment we're only concentrating on his playing, and his playing has been top class."
Carragher joined the Liverpool youth team in 1990 and went on to sign his first professional contract in 1996. Since making his debut in January 1997, he has gone on to make more than 700 appearances for the club.