Emile Heskey has confessed he can 'understand' why a move to might tempt , and insisted any player who says they've not dreamt of playing abroad is 'lying'.
The former striker has expressed sympathy for the club's fans upset at the prospect of the right-back's departure.
As it stands, Alexander-Arnold is set to leave on a free transfer at the end of next month when his contract runs out. Negotiations over a new deal have, so far, been unsuccessful in convincing the 26-year-old to pledge his future to his boyhood club. The defender is mulling over an offer from the 15-time European champions.
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Alexander-Arnold - the subject of an approach from the giants that Liverpool rejected during the winter - has received a mixed reception from Reds supporters recently.
said: "I can understand why the fans and maybe even the club are frustrated by the situation, as Liverpool is one of the biggest clubs in the , so it's hard for everyone to understand why he would want to leave.
"People expect homegrown players to stay with the club forever and cement their legacy like did, and if they do leave, it's on the club's terms, which isn't the case with Trent.
"But I do sympathise with him, I believe all footballers grow up fantasising about playing abroad. When I was learning the game, I dreamt about going and playing in Italy, as it was the best league in the world at the time."
Reflecting on his own career, Heskey, speaking to the via Best New Bingo Sites, added: "I had those ambitions, and I saw Paul Ince and David Platt make those moves, which let you know it was possible.
"So I believe every player dreams of playing abroad and gaining that football and life experience. If a player says they have never even thought about it, they're lying.
"Real Madrid are arguably one of the biggest clubs in the world, alongside Liverpool, so I can understand his interest in moving. At the end of the day, it is his career, and he can do what he likes with it, and if he thinks Madrid is the next step, then he will go."

Alexander-Arnold has repeatedly refused to address his future with the media. Speaking after scoring the winner at last month, he said: "I've said all season, I am not going to speak on my situation.
"I am not going to go into details but these days like today are always special: scoring goals, winning games, being close to winning titles and being in title races, they are special moments that will live for me forever. I am glad to be a part of them."
Following his return from injury, Alexander-Arnold was back in the starting line-up as Liverpool clinched the title with an emphatic 5-1 victory over Hotspur at Anfield. The Reds visit on Sunday.
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