Carragher has ambitions to one day manage Liverpool and was asked a nominee as his imaginary interviewee.
"I love talking about the game, learning things from people, but there's always a mystique about people you haven't had the chance to speak to," he said.
"I wasn't disappointed and got on great with him. He used to make me laugh every day, honestly. It was just the way he was - no messing. I loved that.
"I've also spoken at length with Gerard Houllier and Rafa Benitez about their methods, so if I had to choose someone, it would be Ferguson.
"What would I ask him? How long have you got? All day? I'd just want to find out what he would make of certain situations and how he would react to them. Just how he goes about things, how he makes it all work."