Carragher announced his retirement plans last week.
"Jamie Carragherâ€™s a guy whoâ€™s put his heart, soul and life into Liverpool,â€ť Rodgers told talkSPORT. â€śAs one of the local players thereâ€™s even more pressure on him.
â€śHeâ€™s been outstanding this season, even when he isnâ€™t playing. As a manager itâ€™s a real privilege to work with someone like that because heâ€™s very committed, has got old school values and really respects me and my decisions.
â€śHe works very hard to prove that heâ€™s still good enough to be in the team. Even at 35 heâ€™s still one of the best defenders in the Premier League.
â€śHe hasnâ€™t totally made up his mind. It wouldnâ€™t surprise me if he had a small amount of time away but, over time, Iâ€™m sure heâ€™ll have a role here at the football club.â€ť