The duo clashed live on air in Sky Sports' Super Sunday coverage in box office fashion, as they debated Cristiano Ronaldo's role at Manchester United.
But they did find common ground when predicting who would go on to claim top spot in the Premier League.
"I kind of wrote off Manchester City last year and regretted it because they turned it on from November and won it so easily," Keane told Sky Sports.
"At this moment in time, as brilliant as Liverpool and Chelsea are, I'd go with Man City."
Carragher concurred and also expressed his doubts about his former club's chances of going all the way this season.
"Liverpool have kept a few clean sheets but they've looked a bit open at times.
"I think Man City right now look really strong defensively.
"Liverpool are scoring all the goals but I'd go with Man City right now."
It looks set to be a tantalising title race with just two points currently separating the top three sides in the Premier League table.
Chelsea are a point clear of Manchester City in second place, while Liverpool are two points adrift of the league leaders in third.
Meanwhile, City continue their title defence with a match against a resurgent Aston Villa side at Villa Park.
There promises to be plenty more twists and turns as the season progresses.
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