Hodgson worked with Carragher during his short time in charge at Anfield.
"After retirement I'm sure he will march quickly up the coaching ladder and become one of the country's top young coaches," he said.
Carragher, who is out of contract at the end of the season, has made more than 700 senior appearances for the Reds.
"Having worked with Jamie Carragher it was always evident that he was a model professional who gave everything he had for club and country," added Hodgson.
"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."