Gerrard was named man-of-the-match for his performance in their 2-1 win away to Aston Villa on Sunday, with the England international scoring what proved to be the winner from the penalty spot on the hour.
Carragher, who has announced he will retire at the end of the season, believes Gerrard will commit himself to the Liverpool cause.
"I'm sure Stevie will sign a contract and finish his career at Liverpool the way I've done," said Carragher.
"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.
"It's not just against Villa. He's been doing it for years, scoring at one end, saving at the other."
Reds striker Luis Suarez turned in another impressive performance against Villa, winning the penalty that Gerrard scored from.
Carragher admits the Uruguay international is challenging Gerrard as the best he has played alongside in a Liverpool shirt and believes he deserves to be crowned PFA Player of the Year.
"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," he added.
"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.
"He put in another top performance and shows why he deserves to be PFA player of the year."
Victory over Villa was the third in four games for Brendan Rodgers' side but Carragher is playing down talk of Liverpool securing a European berth next season.
"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," said Carragher.
"Sometimes it is fifth spot, sometimes sixth, seventh. We just will try and carry on and win games and see where it takes us."