It is true that Trent Alexander Arnold mentioned that Barça was one of his favorite teams back in 2020, he did not choose to mention the club over Liverpool. To quote him directly, he stated: "My other favorite team would be Barça. I feel as though they have the same values and beliefs as Liverpool." It is typical for footballers to be fans of teams other than their own when they are young (i.e. Luka Modric being a Barça fan as a young boy). In the same interview with GQ UK that he said the prior statement in, Alexander-Arnold was asked the following question: "But would you fancy playing in Spain or Germany?" to which he replied "I’ve always loved Liverpool. I’ve always supported them. I’ve always played for them. So, I’ve never had that reason to think about it. Yeah, still now, I wouldn’t sit there in my room and daydream about playing somewhere else. Right now, I’m a Liverpool player. I love the club more than anything." Therefore, Alexander-Arnold was not emphasizing his liking towards Barça over that of Liverpool, in fact, he would not and has not considered playing under another badge that is not Liverpool.
https://www.gq-magazine.co.uk/lifestyle/article/trent-alexander-arnold-interview
