Sky Sports pundit Carragher, who played 737 games for the club between 1997 and 2013, has also backed Henderson to replace Steven Gerrard as Liverpool captain after he leaves for the MLS at the end of the season.
Henderson, a £20m signing from Sunderland in 2011, is the latest first-team player to commit his future to Anfield, following Daniel Sturridge and Philippe Coutinho.
“This is big news,” Carragher told Sky Sports. “I would imagine next season he’ll be the captain.
“He’s done an excellent job when Steven Gerrard’s been out, not just in his own performances, but the team’s results have been very good which always helps.
“He’s young, he’s English, he’s never injured and he’s improving all the time. He’s getting more goals and more assists, is becoming more influential in the team and I only see him getting better in the next four or five years.”
Liverpool are also understood to be close to completing new deals for Martin Skrtel and Jordan Ibe.