I can see why they would try to sign a free agent like Alexander Arnold to equip themselves also for the future. It would be the right call in my opinion, but competition for that player will be fierce and he can already be looking forward to signing the best contract in his life. 125 million net for five years and a signing bonus of tens of millions on top of that.
It would be stupid for Liverpool to let him go for free though. If he's not willing to stay maybe they will sign a contract with a buyout clause or something similar so Liverpool will gain something from him. I would be surprised if that's not the case considering how much the owner likes to use transfer money to buy new players.
Anyway, the funny coincidence is that some players who exit Liverpool usually fail to perform at their best. Wijnaldum, Mane at Bayern, Coutinho etc. Of course, exceptions exist, and each situation is different but it would be interesting to see if Arnold turns out to be the same or not. If he ever goes out that is.
The club cannot force Trent Alexander-Arnold to extend his contract in Anfield. If he has interest in moving to Real Madrid, it will be difficult to persuade him to remain in Liverpool. I will blame Liverpool for allowing a player of his quality contract to be close to contract expiration before plans are made for renewal. His contract should have been extended two years before the end.
It is believed that Real Madrid is willing to give the England international a long-term contract for about five years with an annual earning of £14-15 million, which is double what he gets from Liverpool. Except Liverpool can convince him and give him a better deal, he might move to Santiago Bernabéu.
There are also reports that Liverpool is already seeking the defender's replacement. The club have started targeting players like Jeremie Frimpong, Vanderson and Michael Kayode as potential replacements.