The 30-year-old Liverpudlian would like to see American owners George Gillett and Tom Hicks appoint a figure such as former manager Kenny Dalglish to a senior role to help with key decisions.
Hicks and Gillett last year revealed they had sounded out Jurgen Klinsmann with a view to succeeding manager Rafael Benitez should the Spaniard leave, but admitted having limited knowledge of the German.
Carragher, writing in his autobiography 'Carra', printed in the News of the World, said: "What worries me about Hicks saying he'd never heard of Klinsmann is this: what happens when we do need to appoint another manager?
"Liverpool fans will shudder at the idea of names being checked on the internet.
"If Kenny was on the board, the owners would be able to ask his advice in the knowledge he has a grasp of what supporters here expect."