The vice-captain has a year left on his current contract and Roy Hodgson wants to quickly sign Carra up to a new deal.
"I'm sure it [a contract extension] will be a priority. Quite frankly so much has happened in the last five weeks, the hours I've spent at the club are enormous, that we haven't actually got round to discussing contracts with players," said the boss.
"I now know that Carragher has got one year left. I can see players like Jamie Carragher and Steven Gerrard never leaving Liverpool Football Club."