During a chat on Sky Sports, Reds legend Carragher claimed that the Spanish giants should pay a sum of £10 million ($13m) to the Merseyside club if they want Alexander-Arnold.
Carragher first said: "And then the flip side of that is, okay, you're announcing it now to give Real Madrid the opportunity to maybe sign you for the Club World Cup, so that's what I was talking about a couple of weeks ago."
Neville then quickly remarked: "Would you take like a million quid if you were Liverpool for the Club World Cup?" Carragher then replied: "Er, I think I'd want more than a million quid."
Neville then further asked: "But would you take, would you take whatever price it would be to let him go and play in that tournament?" To which Carragher replied: "I think if it was about five or ten million quid, because I think I could get, no, hang on, hang on."
The Sky Sports host then asked: "What is it, a hundred million to win the thing?" In reply, Carragher said: "Exactly. Have you seen how much money it is to win it?"
The host then continued asking: "So you could help a major European rival by helping them win the thing?"
The Liverpool icon then responded: "Right, well, but if they're going to win a hundred million and he's going to help them, because don't forget, they haven't got any right back. The right back to play in there is not a right back. So it's not just like bringing a player in. Give us ten million quid."
Neville concluded the conversation by saying: "Well, the price has just been set, mate."