The former England international, who has announced that he will retire from the game at the end of the season, has been tipped for management or TV punditry work.
"He works very hard to prove that he's still good enough to be in the team," Rodgers told talkSPORT. "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."
Carragher has spent 17 years at the Merseyside outfit.