However, they have become good friends after hanging up their boots.
The duo both became pundits with Sky Sports and they now get on very well.
Neville has a YouTube channel named The Overlap where he conducts interviews with big names in the sporting world.
He has previously spoken to names including Roy Keane, Anthony Joshua and Tyson Fury.
The latest person to appear was Carragher.
Neville has asked Carragher 23 'quick-fire' questions while walking around Liverpool in a brilliant video. Watch it below.
We've listed some of the best questions and answers below...
What was your pre-match ritual?
Carragher: "Read the programme. Always read the programme on the toilet. Not just on it..."
What was the worst game you've played?
Carragher: "There's been a few... two own-goals against Manchester United (in 1999). Some against Thierry Henry..."
Messi or Ronaldo?
Torres or Suarez?
Carragher: "Suarez. Unbelievable. I thought he was the best centre-forward in the world for three or years. That last year at Liverpool and what he did at Barcelona for the next two or three years.
"He leaves Barcelona and then wins La Liga with Atletico Madrid. He gets to the semi-final of the World Cup with Uruguay. That Liverpool team that nearly won the league was an average team. He nearly single-handedly took them to the league. That's what he does with every team he goes to."
Rafa Benitez or Gerard Houllier?
Carragher: "Benitez was a better manager, but Houllier was a better man-manager. I'd probably just edge for Benitez because of what we achieved and me personally playing centre-back and my best football."
Best Premier League player of all-time?
Carragher: "Thierry Henry".
Who do you want on a last-minute penalty?
Carragher: "Steven Gerrard".
Who was the funniest player you've played with?
Carragher: Craig Bellamy. He was very, very funny. The things he would say to people, I couldn't believe. Some may say it was too much - sometimes it was too much - but we had a very good relationship.
"I found him hilarious. He was a brilliant trainer, he loved his football. He was very cut and very sharp."
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Phil Neville or Gary Neville?
Carragher: "Gary. It's got to be Gary."