Carragher announced his retirement plans last week.
"Jamie Carragher’s a guy who’s put his heart, soul and life into Liverpool,” Rodgers told talkSPORT. “As one of the local players there’s even more pressure on him.
“He’s been outstanding this season, even when he isn’t 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 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 defenders in the Premier League.
“He hasn’t totally made up his mind. 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.”