Rodgers has revealed he faces a struggle to prevent defender Carragher from retiring at the end of the season.
"Jamie's contract is up and we've had loose discussions in terms of where he's at," said Rodgers.
"It is largely down to him and how he's feeling.
"When you've played so long at the top level and been a key figure, and then don't have a period of playing so much, it gives you some thinking time, 'Do I want to put my body through this every day and not have the games I'm used to?'
"You're in the firing line at the back. There is no hiding place for a centre-half. It is not an easy decision for him but do I want him here? Of course."