The former Reds centre-back wants to see the Manchester United forward replicate his club form for the Three Lions.
Carragher told Sky Sports News: "Wayne Rooney has been the standout player for England for a long time now alongside [Liverpool captain] Steven Gerrard.
"He's still a top player and I think going into an international tournament, he now needs to show what he's all about. He's had two or three tournaments where he's not really hit the heights that we know he's capable of.
"Now, as he reaches his prime years, he should be looking to dominate a tournament."
Rooney signed a new contract with United on Friday to become the highest paid Premier League player of all time.