The pair were there to provide punditry for the fourth Ashes Test at the SCG in Sydney when Joe Root's future as England Captain became the topic of conversation.
Ali seemed to take a jab at Cook's player management skills during his time as England captain.
The spinner, who has played under Root and Cook, defended his captaincy before taking a jab at his fellow pundit. He said: "Rooty has a bit more of an emotional attachment with the players, he spends more time with the players".
This jab directed towards Cook certainly drew a reaction, he said: "Are you just criticising my captaincy?".
Ali replied with: " I am a little bit, yeah. They're both very different. I did much better with the bat under Cooky, but with the ball, I was better with Rooty".
Cook was having none of it, replying with: "I have to say, I never dropped Mo.
"So he might criticise me but I never dropped him. How many times did Rooty drop you?". He continued.
Ali fired back with: "To go back to my point, Rooty was a little bit more involved with the players, in my opinion. Not that Cooky didn't care, but I think Rooty is a bit more of an 'arm over the shoulder' kind of guy".
The former England captain tried to make a joke about it, but you could see the shock and embarrassment plastered across his face.
He said: "I'm not sure how to take this anymore.
"I've just come back from a nice holiday, and I've walked straight into Moeen Ali off his long run".
On his return to the test side, Usman Kawaja hit a fine 137 runs to propel Australia to a 423 run first innings score.
England currently sit 13-0 at the end of day two at the SCG, batsman Zak Crawley survived a late scare after being caught behind a no-ball bowled by Mitchell Starc.News Now - Sport News