Gerrard, 32, deservedly won the man of the match award in Liverpool's 2-1 win at Aston Villa on Sunday and scored the winner from the penalty spot.
Carragher said: "I'm sure Stevie will sign a contract and finish his career at Liverpool the way I've done. There is no doubt about that. I'm sure he'll sit down and sort it out in the next couple of months. Steve will be finishing his career at Liverpool. He is 'captain fantastic' every week."
Liverpool boss Brendan Rodgers has confirmed he will hold talks with Gerrard over a new contract and is convinced he can play into his late 30s.
Carragher, who is retiring at the end of the season, admits striker Luis Suarez is now close to rivalling Gerrard as the best player he has played alongside for the Reds.
The spot-kick against Villa was awarded for a challenge on Suarez who shrugged off the tiredness from his World Cup qualifier exertions and travelling with Uruguay to produce another dynamic performance.
Carragher said: "Every side has a couple of players in the side you hope can turn things for you and Luis does it on a weekly basis. I've played with a lot of top players here and I've always said Stevie was the best player I've played with. But Luis is definitely on his shoulder, he is very close."
Liverpool came from behind to win a Barclays Premier League game for the first time in two years with Jordan Henderson cancelling out Villa striker Christian Benteke's opener.
It was their third victory in four games but Carragher is playing down talk of challenging for a European spot.
He said: "Winning that game (against Villa) now makes Southampton look like a blip because we were on a good run. But I don't really look too far ahead and to be honest if you asked most of the lads, they wouldn't even know what position would get us into Europe."