On 31 March Carragher stated his desire to stay at Liverpool for life having said days earlier that he would have "no problem" in leaving the club.
The defender made his Liverpool debut in 1997 and has played nearly 600 times for the club, also winning the Champions League in 2005.
"I now know that Carragher has got one year left," added Hodgson, who only took charge of the club last month.
"Quite frankly so much has happened in the last five weeks. The hours I've spent at the club are enormous, but we haven't actually got round to discussing contracts with players.
"That's the only contract of a player that I know about - if you asked me how many years the others have got, I haven't got a clue.
"I can see players like Jamie Carragher and Steven Gerrard never leaving Liverpool Football Club. I can see them always being part of the club."
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