The defender is set to hang up his boots following Sunday's game against QPR having player 738 times for the Anfield club, and the Rs boss says he ranks among the club's best
The 35-year-old will play his 738th and final game for the Reds on Sunday against the Rs, bringing a 17-season playing career at Anfield to an end.
And after winning five domestic cups and four European cups - including the Champions League - Carragher is up there with the best Liverpool have ever produced, according to Redknapp.
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"Everybody would love a Jamie Carragher in their team. If I had him in my team next season we'd get promoted. That's how highly I rate him.
"He's the type of player who will drag the team along for you. There aren't many of them around. Liverpool are very lucky to have had him and Steven Gerrard at the club. They've been brilliant.
"Liverpool's his team and I imagine he's never even thought about leaving the club. It will be a full house for him at Anfield.
"He's been massive to Liverpool, one of their most important players. He's up there with all their great players over the years - Tommy Smith, Emlyn Hughes and Phil Thompson."
Carragher also represented England 38 times during his career - including at the 2006 and 2010 World Cups - before retiring from international football in the summer of 2010.