The 35-year old has set a date for his retirement, which will occur at the end of the season, and Hodgson has suggested that his next chapter of life could be as a coach.
"Having worked with Jamie Carragher it was always evident that he was a model professional who gave everything he had for club and country," he told TheFA.com.
"He has had a fantastic career and will always be looked on very fondly by everyone associated with Liverpool Football Club.
"It was good to see him back in the team recently, I hope that between now and the end of the season he is able to add to his great total of appearances for the club.
"After retirement I am sure he will march quickly up the coaching ladder and become one of the country's top young coaches."