As a Liverpool fans actually i don't want to see Alexander-Arnold moved from Liverpool especially he came from Liverpool Football Academy so he was playing with Liverpool since at junior team besides that Liverpool currently is very solid and Alexander-Arnold as part of Arne Slot plan but apparently Liverpool has no plan to give him contract extension which mean possibly Alexander-Arnold will be leave with free transfer status and since last summer actually Alexander-Arnold was linked to Real Madrid especially Jude Bellingham which Alexander-Arnold close friend has been invite him to joining with this team
Of course, releasing Alexander Arnold is a loss for Liverpool, but currently he has not renewed his contract which will expire in January next year. So the possibility is still unclear, but Madrid will definitely look for a replacement for Carvalaj. Of course, Ancelotti has to wait for the winter market to open, maybe an alternative can also be taken from Real Madrid's young players. Of course, they have to use the players they have at the moment and make the player collectivity better and minimize injuries. Another problem, indeed Madrid was not very active in the last transfer season.
When a player has not extended his contract, it means that he is still wide open to leave the club. Those interested in Alexander Arnold are not ordinary clubs, they are big clubs that are even the most successful clubs in the Champions League, that will certainly make Arnold consider whether he will stay or not if Liverpool offers him a contract extension. On the one hand, Liverpool is also a big club, so it will be quite difficult for him to make a decision. However, at this time I have not heard that Real Madrid is serious about approaching him, the rumors circulating only say that they are interested in this player. And now we also have to wait until the transfer window opens. However, Real Madrid could make a quiet move.