Rooney remained at Manchester United following a summer of discontent which saw a move to Chelsea fail to materialise.
The 27-year-old striker scored his 200th goal for the Red Devils in Tuesday's 4-2 Champions League win over Bayer Leverkusen, and Carragher, who played alongside Rooney for the national side, thinks he now needs to look at the bigger picture and secure his place in history.
"Wayne has endured a difficult summer but now the speculation about his future is over, it is time for him to sign a contract and become a legend," Carragher said in his column for The Daily Mail.
"He has made a fantastic living and won more medals than most could dream about but he has to look at the bigger picture now.
"His next challenge must be to put himself among Old Trafford's gods. He must ensure that, in years to come, he is spoken about with the reverence that is reserved for Sir Bobby Charlton and George Best, Ryan Giggs and Eric Cantona."
Charlton currently leads United's all-time goalscoring standings with 249, but with Rooney in his prime, Carragher is confident he can pass that total - as long as he can outperform team-mate Robin van Persie.
"Standing tantalisingly in front of him is the chance to set a record that could stand for ever," Carragher said.
"He could become Manchester United's all-time record scorer. What an achievement that would be. Lots of players have been multiple medal winners at Old Trafford. Only one can be the highest scorer.
"I'm delighted he stayed at United because I did not understand why he wanted to move. Why risk all he has built for a few years with Chelsea? To be the 'main man'?
"If he wants to be the main man at United again, as he was a couple of years ago, the answer is simple: outperform Robin van Persie."