Alexander-Arnold was one of three senior Liverpool players – alongside captain Virgil van Dijk and talisman Mohamed Salah – to enter the final year of their contracts last season.
Van Dijk and Salah ended up signing new two-year deals in April, after which the spotlight turned solely on the England defender.
Posters were put up outside the ground by disgruntled supporters, questioning his loyalty to the club where he had won two league titles, as well as the Champions League, Fifa Club World Cup, FA Cup and Carabao Cup.
“I think whichever way I am received is the decision of the fans,” added Alexander-Arnold. “I will always love the club. I will always be a fan of the club. I will always be thankful for the opportunities [Liverpool gave me] and everything that we achieved together will live with me forever.”
He also said he would not celebrate if he scored against Liverpool and revealed many of his former team-mates got in touch when the Champions League draw was confirmed.
“I spoke to Robbo [Andy Robertson], Mo [Salah], Ibu [Ibrahima Konate],” added Alexander-Arnold. “They were just laughing. I think everybody knew it was going to happen. We will put our emotions to one side and play the best football we can.”
Alexander-Arnold has only recently returned to the Real Madrid squad after recovering from a hamstring injury suffered in a Champions League tie against Marseille on 16 September.
But he has yet to make an appearance in the side and likely to start on the bench against Liverpool as 15-time European champions Real – managed by another former Reds player in Xabi Alonso – bid for a fourth successive win in this season’s competition.
Alexander-Arnold has endured a difficult time since his Madrid move, struggling to establish himself in the first team, being left out of the England squad and sidelined by injury.
But he praised Real’s England midfielder Jude Bellingham for helping him to adapt.
“He is a great lad and a great friend,” said Alexander-Arnold. “It’s good to have someone else that is English here. We both understand each other very well and know each other very well. He made settling in a lot easier for me.”