The former Reds defender has been a regular fixture on television screens across the country since hanging up his playing boots after taking up a role as a pundit with Sky Sports.
The ex-England international revealed that he has not yet been offered a managerial job in the Football League and suggested that it would take a significant offer for him to be tempted away from his hometown of Liverpool.
And Carragher says that he would open to taking up a coaching role under Klopp at Anfield.
Former England defender Carragher told the Daily Mirror: “I’ve never been offered a full-time role at a club or management or anything like that.
“If it was something that you really fancy, I suppose, but when I say ‘fancy’ I mean I would have to move from Liverpool. My kids are at school there, so I’m basically waiting for Jurgen to give me a call!”
Liverpool, who appointed Klopp as Brendan Rodgers’ successor at Anfield back in October, are currently gearing up for their League Cup final clash against Manchester City at Wembley at the end of the month.
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