Carragher is struggling to command regular first-team football and has entered the last season of his contract.
"Jamie won't be fully appreciated until he's gone," said Gerrard to the Daily Mail. "When you're local I think it can get overlooked, how important you are in the set-up. He does so much for the club on and off the field.
"The kids here really look up to him. The stuff he does in his spare time, he's a real role model for the club and I don't think everyone fully understands what that means.
"I'm sure the club realise and, hopefully, they will do their best to keep him around. He performs such an important role here."