Real Madrid, the most successful club in European football history, never miss an opportunity to get the best players in the world. Los Blancos' current president Florentino Perez likely never misses out on his big targets. After setting an eye on English Full-Back Trent Alexander-Arnold, it looks like they will eventually get the defender from Liverpool.

The Trent transfer saga:

Real Madrid's interest in the English Full-Back has grown day by day. However, they still have a couple of Full-Back options in the form of Dani Carvajal and Lucas Vasquez.
Including, they have an academy-grown option in the form of Raul Asencio. After Jurgen Klopp announced his departure from The Reds, it seems likely that some of their certain figures are submitting wishes for the transfer. More likely the names are Virgil Van-Dijk, Mohamed Salah, and Trent Alexander-Arnold.
The Reds are offering Contract extensions to the trio which is ending after the 2024/25 season. However, according to the reports, none of those players are showing any kind of interest in the contract extensions. Richard Hughes, the current sporting director of Liverpool FC is fully focused on signing the important trio of Van Dijk, Arnold, and Salah.
So, the reports via English and Spanish media look baseless, and some of their reports still look lost by Liverpool's managerial statements. Moreover, some of the reports are just claiming that the Trent to Real Madrid saga is just a rumour.
Why this move makes sense:

The end of the 24/25 season is near. Alexander Arnold's boyhood club is Liverpool and after being a graduate of the Red Academy graduate, he is more likely to have a secret willingness to join the Los Blancos. His playing style, and ability to orchestrate the attack this kind of playstyle would be a perfect piece of Carlo Ancelotti's Madrid lineup.
In the absence of Dani Carvajal in Carlo Ancelotti's Madrid, they need an attacking full-back and a replacement for Dani. Carlo Ancelotti's Los Blancos does not get any time to replace the injured Dani Carvajal. Real Madrid needs a plan on the right side of the defence.
Arnold's reaction to the transfer saga:
In the English Premier League match against West Ham, after scoring the 5th goal for the Reds he ran toward the corner flag in celebration and made a gesture about the transfer saga rumours between him and the Los Blancos.
Things move quickly in the footballing world. In the recent clash against Manchester United on 5th January 2025 at Anfield, the Reds just managed to get one point against the Red Devils. Arnold's game is not up to the mark and fails to fulfil Arne Slot's game plan. Seven days after the West Ham goal and the victory, Madrid offered 25 million euros for the English full-back to add him to the Los Blancos in this transfer window. But seems like the full-back is going to join Real Madrid as a free agent or more likely he will join the European giants in the next transfer window.