The 27-year-old has been in fine form for Liverpool so far this season, hitting five goals in the Premier League and eight in all competitions.
The Senegalese joined Liverpool from Southampton on a five-year deal in June 2016.
According to Carragher, it has been a while since Liverpool had a world-class winger and Mane is precisely the kind of player the Reds needed.
"Even after the first couple of games, I said Mane, probably along with Raheem Sterling, was possibly the best left winger in the world," he told Liverpoolfc.com.
"I absolutely love him, he's my favourite player at the club. He's brilliant, he's always got a smile on his face, always there, always gets knocked about, and gets goals, setting others up”
"He's the one who came in at the very start under Klopp, his first real big signing, and I think ever since then he's just been getting better and better. He's just a machine."
Jamie compared Mane’s impact to that of former Liverpool winger John Barnes, who spent a decade at the club and won two league titles.
"I always talk about the teams I played in never possibly had, say, a John Barnes, that world-class wide player," he added. "But I think Liverpool have got that now.
"I think that's what's making the difference why they are so good and look in a great position to hopefully go on and win the first Premier League.
"If you start comparing people like Sadio Mane to John Barnes then that shows how well he's doing."
Mane scored his 50th Premier League goal for Liverpool last weekend in their 2-1 win over Leicester City.
