Rush sees Carragher as future Liverpool manager
Carragher, 35, announced he will retire at the end of this season.
Former Liverpool and Wales ace Rush says the defender should stay at Anfield in a coaching role before taking the reigns himself.
He said: "Hopefully one day he will become a manager and hopefully that will be of Liverpool.
"I'm pretty certain he's got the qualities to be that.
"He's a winner and if he can instill that in the players that's when you become a good coach."