The Chelsea defender was stripped of the armband last week and the fall-out has seen Fabio Capello resign from his role as Three Lions manager.
One of the first jobs the next England manager will have to do is choose his on-field leader and Carragher believes there is only one man for the task.
Asked if he Gerrard would want the captaincy, his Liverpool team-mate told Drive Time: “Yeah, I would imagine so. Anyone within that squad, I think, would love to be captain.
“Maybe a new manager comes in and has different ideas. Who knows who the manager will be? He might see things differently, but for me Steven Gerrard is the stand-out captain, and that’s not a biased verdict.
“He’s been the captain of Liverpool for probably a decade. He’s captained in Champions League finals, Europe, big Premier League games.
“He’s also captained England in the last World Cup and he’s one of England’s best players. So, for me, I don’t think there’s a debate, if I’m being totally honest about it.
“[It should be] Steven Gerrard without a shadow of a doubt.”