Alexander-Arnold, 28, left boyhood club Liverpool for the bright lights of Real Madrid last summer in one of the more controversial transfer sagas in recent memory.
The right-back was an undeniable star at Anfield. No defender in Premier League history has provided as many assists in the competition as Alexander-Arnold (64).
It’s not quite worked out for the England international in the Spanish capital, however, starting just three of his six LaLiga games so far this season, a grand total of 266 minutes.
Liverpool fans weren’t happy with Alexander-Arnold’s decision to leave, but Carragher now believes a return needs to be on the cards.
"I would bring him back," Carragher said as quoted by AS.
"He would get a lot of criticism, because I think he made a mistake. I think he made a big mistake going to Madrid. We (Liverpool) have certainly missed his creativity.
"At the moment, he is the third option at right-back (for Madrid). They are playing a midfielder, (Federico) Valverde, in that position; even in the Clasico, Denzel Dumfries, the starting right-back, came on ahead of him.
"When you are the third option at a club, obviously they want you to leave."