The former Liverpool defender turned pundit thinks the youngster signing a new contract is essential to the club's future.
The young forward is yet to agree a new long-term deal at the club, with his representatives and those higher up at the club reportedly negotiating new terms for the last three months without success.
The Guardian had reportedthat Liverpool chief executive Ian Ayre had been holding talks with Sterling and his representatives earlier in the month and that a deal was close, but talkSPORT's Warren Haughton, denied that a contract was anywhere near being signed.
Now, Sky Sports pundit Carragher has said that getting the youngster tied down to a new long-term contract, akin to that recently signed by Philippe Coutinho, is vital to the club.
“Every time the manager is asked about it he says his agent and the people at the top of the club are dealing with it,” Carragher said on Sky Sports.
“He’s a very young player, one of the top players in English football. I think for everyone at the club the quicker it is done and dusted with the better.”
The former defender believes that the club must ensure that Sterling, and other talented youngsters such as Coutinho, have to be tied down to the club for the long-term as soon as possible, especially now that Steven Gerrard is leaving at the end of the season.
Gerrard has of course agreed a deal to join MLS side La Galaxy at the end of his current contract, and these types of players must be given the opportunity to one day become an iconic player like him.
“You need to keep these players at your club,” added Carragher.
“You’re losing an iconic player in Steven Gerrard at the end of the season so it’s important you keep these young players and hopefully one day they can be an iconic player too.”