He said that he only wants to win trophies, I also think that he would like to extend his contract with Liverpool, but since such an offer has not followed, he will wait for other offers and he certainly will not be against becoming a Real Madrid player if he receives such an offer. He can go to Real as a free agent, Real Madrid manages to negotiate this with players, as they did with Mbappe, as PSG did not try to persuade him to stay in the team, he rejected all offers. If Alexander-Arnold wants to become a Real Madrid player, then nothing will stop him from doing the same.
Alexander-Arnold is not only a right-back but he is also one of the sources of creativity in Liverpool's attack and losing him would be very detrimental to Liverpool. Some reports that I read in the media Liverpool gave up on Alexander-Arnold's contract extension and they opened the opportunity for negotiations with Real Madrid but so far there has been no clarity. Unlike Mbappe's status who in reality does not want to stay at PSG so that the effort to negotiate a contract extension was unsuccessful because previously PSG had extended Mbappe's contract for one season.
Arne Slot has always avoided answering questions about Alexander-Arnold future, although everyone knows that the player contract will expire in June 2025. Liverpool will certainly try their best to persuade him to stay at Anfield, amidst Real Madrid increasing interest. Letting him go in the January transfer window will reduce Liverpool bargaining power in every competition, indeed the Reds have Conor Bradley as a backup player, but it seems that he still cannot convince Arne Slot to occupy the right-back position regularly.
Actually, Liverpool are faced with a dilemma, Alexander-Arnold plays a key role in the negotiations, because staying or leaving all depends on himself. What is clear is that Liverpool do not want to lose out with Alexander-Arnold leaves on a free transfer.
Real Madrid want to make Alexander-Arnold a long-term plan, and for now, they really need a right-back after Carvajal suffered a serious injury. We have often seen, it is difficult for every player to refuse an offer from Real Madrid, Florentino Perez has a thousand ways to tame the player he is targeting.