The Cardiff City veteran is being linked with the Wales job.
Carragher wrote in the Daily Mail: "He is very intense and driven but he could also bring humour to the dressing room and is one of the few players who shared my enthusiasm for the game and that is why I expect him to one day go into coaching and management.
"So with the passion he has for his country, it really wouldn't surprise me if, in the future, he became Wales manager.
"Craig should feel proud of what he has achieved for his country - and I fully expect him to be there for them again at some stage."
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