Carragher is no longer an automatic choice for the club he joined at the age of 13, but Rodgers said: "Jamie still has a lot to offer this club - and he is in such great physical and mental condition that he could carry on playing here for a few more years.
"Of course, the time comes for even the greatest players to sit down and think about what they want to do once they have stopped playing.
"Jamie is a great student of the game. He can go down whatever route he wants and I am sure the club will sort that out for him when the time comes.
"Whether it is coaching, scouting, or recruitment is up to Jamie. But whatever it is there will be a role here for him because he is an iconic figure at Liverpool."