Carragher and Keane's angry exchange on Sky Sports attracted millions of views on Sunday and millions more on the network's social media channels since then.
"You see a guy who’s won everything in the game, he’s come back to Man United to try and lift the club. Course he’d want to play," stated Keane.
"You still think if Ronaldo’s on the pitch, if the ball falls to anybody in world football - even at 36 - it’s Ronaldo. It’s not as though he’s come back to the club and not scored.
"Ronaldo’s not going to fix Man United’s problems, but you don’t bring him back to sit on the bench."
Carragher offered an alternative view, as he insisted Ronaldo does not need to play in every match despite his superstar status.
"PSG have signed Messi, United have signed Ronaldo," Carragher argued. "Two of the greatest players of all time.
"Are Man United closer to the league title now than last season? No. Are PSG closer to the Champions League with Messi in the team? No. It’s a team game, football."
Now Ferdinand has joined the debate, as he hit out at Carragher's failure to win a Premier League title during his career, as he offered up these comments on his Vibe With Five podcast.
"Carra shouldn’t really be talking about winning league titles, he’s never done it," said Ferdinand.
"He don’t know what it means, he didn’t know how to do it, he’s never navigated a team through it to that point to win a league.
"So I find it very difficult when he speaks with such conviction about winning leagues. He should stick to cup competitions. When he talks about winning leagues, I just mute it."
Carragher was quick to respond, as he offered up this tweet by way of a repost:
The spat between Ferdinand and Neville has clearly been fuelled by the latter's tweet mocking Rio's comments urging United to give Solskjaer the Old Trafford job back in March 2019.
Ferdinand even referenced this tweet from last week when he posted his response to Carragher on Monday:
Ferdinand then invited Carragher to come onto his show next week, as he hinted his rant was a very well orchestrated publicity stunt for his YouTube channel: