“We are losing one of the greatest managers in world football, one of the greatest managers Liverpool have ever had and it is a sad day, no doubt,” Carragher told Sky Sports.
“But in the same breath, we’ve got to be looking forward to the new man coming in, get behind him and support him. Bill Shankly left, Bob Paisley left, Kenny Dalglish left and Liverpool moves on.
“You can’t get away from Xabi Alonso because he’s so respected at Liverpool already for what he did as a player – he’s a Champions League winner, held himself with real class, he’s a World Cup winner.
“Right now, the job he’s done at Bayer Leverkusen, he looks like the brightest young thing in European football. It certainly makes him the front-runner.”
Liverpool have a five-point lead over Manchester City at the top of the Premier League – albeit having played a game more – and are into the Carabao Cup final and still in the FA Cup and Europa League.
Carragher, who made 737 appearances for the Reds, posted on X, formerly Twitter: “This news was always going to be a body blow to the club whenever it came.
“I just thought it would be another few years away. What a manager, what a man, let’s go out with a bang Jurgen!”
His thoughts were echoed by ex-Reds striker Michael Owen, who posted: “All great things inevitably come to an end but I thought it would be 2 or 3 years down the line. Memories to last a lifetime. One of the greatest managers ever.”
Bayern boss Thomas Tuchel, who succeeded Klopp at Borussia Dortmund in 2015, said he was still trying to “process” the news when asked about it at his pre-match press conference on Friday, but added: “Kloppo is one of the best coaches of all time. He’s always managed to influence an entire club at all his clubs. It’s huge news.”
Klopp’s Manchester United counterpart Erik ten Hag hailed the “amazing job” the German had done on Merseyside.
“He has made an era there. He built the club, he brought the club back I think where they belong, so congratulations on that,” the Dutchman said.
Liverpool host Norwich in the FA Cup at Anfield on Sunday.
Canaries boss David Wagner has known Klopp for more than 25 years after being team-mates at Mainz, and was best man at his friend’s wedding.
“I wasn’t surprised when he told me,” Wagner said at Norwich’s pre-match press conference on Friday afternoon. “I was happy for him, because I know how hard and how difficult for him this decision was and is.
“It shows a lot of personality, character and bravery as well. Only he knows what is best for him.
“We all know how exhausting and how challenging this business can be. If he knows it is best for him then I am happy for him and he will have a great time in front of him for sure.”