With the teams playing at Anfield on Sunday the pair of pundits were tasked with selecting a composite XI for their former teams.
And Neville revealed on Sky Sport he would have Pogba in a holding midfield role, despite him not starting the most recent match against Arsenal.
Carragher responded: "Holding what? He's the most undisciplined player of all time!"
Neville back-tracked slightly, admitting that his affinity for his former club played a part.
"I didn't pick him with much conviction to be honest with you," he added. "I was clutching at straws. Matic. Jordan Henderson and James Milner they're in and out of that midfield in terms of playing."
"I wasn't convinced by anything just through what's been happening. I just thought it's an opportunity for me to put a United player in to be honest!"
As for Carragher, he only selected David De Gea and Nemanja Matic from United's squad.
In their combined team, however, that number increased to three United players - not surprising, given United trail Liverpool by 16 points already in the Premier League.