Carragher cited Owen as further evidence of the situation Alexander-Arnold may one day find himself in should he sign for Los Blancos.
"On the other hand, he could go to Real on the kind of huge wages that free-agency players can command and win Champions League and La Liga titles there," the former centre-back added. "That too will sound pretty good for a footballer – but it is then what comes next. It is a long life after you finish playing. How people treat you in the city from which you come makes a big difference. And fans do not care that you made millions more. For them, that salary is irrelevant.
"On top of that, as a local lad, you are always treated differently. We saw it with Steven Gerrard. Even contemplating leaving for Chelsea on two occasions in his career temporarily damaged his relationship with Liverpool fans. Was it fair? It was simply the reality with a passionate, tribal fanbase.
"My team-mate Michael Owen had one year left on his contract when he joined Real from Liverpool in 2004. He too was in a struggling Liverpool team with a new manager coming in – Rafael Benítez – and a good deal of uncertainty. Again Real paid only £8 million for a footballer who was worth much more. Michael’s time at Manchester United later in his career would have done more damage to his legacy but still – the terms of his departure to Real did not help."