Carragher only recently admitted his career may soon be coming to a close, and has made no secret of his desire to enter coaching when he eventually retires.
Already, the 33-year-old centre-back is in the process of earning his UEFA B licence, and Smith is confident Carragher will be a top manager regardless of who he takes charge of.
"It was interesting to hear Jamie Carragher on his plans when he eventually hangs up his boots," Smith said on Liverpool's official website. "And no surprise to know that he wants to stay in the game and get into management.
"Because Jamie will not just make a good manager one day, but a good Liverpool manager, of that I have no doubt."
"I was fortunate to play for years under Bill Shankly, Bob Paisley and Joe Fagan. And if you don't know what makes a good boss after playing under those men, you'll never know.
"They were all different but all had fantastic strengths, a passion for the game and a love of Liverpool FC."
And Smith believes Carragher, who has been a tireless servant for the club over the years, is cut from the same cloth as Liverpool's legendary managers.
"Not one of them would tolerate a player giving anything but his best, week in, week out. They were born winners who loved the fans and reminded their players of their duty towards them.
"Shanks in particular worshipped the fans as much as they loved him.
"All sound familiar? They are exactly the qualities and characteristics which Jamie Carragher possesses in abundance."
Carragher is currently second in Liverpool's all-time appearance list after making 676 appearances for the club, and Smith believes the former England international not only has the passion, but the experience and mentality necessary to succeed as a manager.
"He's doing his coaching badges now but given all his experience at Liverpool and on the international stage, he's already perfectly well-qualified for me.
"Jamie not only loves the club and knows it inside out, he also has a fantastic knowledge of the world game too. He's not just a wholehearted local player as some see it, but an educated student of the game. And that's important too these days.
"Jamie wouldn't stand any messing from anyone, and as we all see he is a born organiser too.
"I've no doubt that one day he'll be be our manager. And rightly so.
"He's got everything we'll one day need in a future Liverpool FC boss."
Carragher has won the FA Cup twice, the League Cup three times, and the UEFA Champions League in 2005, but is still searching for his first Premier League title.