Roy Hodgson's name is understood to be top of the Anfield board's list, with former player and boss Kenny Dalglish also showing an interest.
Thanking his outgoing manager and hoping for a swift replacement, Carragher said: "I would like to thank Rafael Benitez for what he did for me and wish him luck at Inter Milan. Hopefully we can get a manager as quickly as we can, then we can start to look to the future."