Real Madrid have always have eyes on good players and cross-check the signings they've made previous season, it's actually been great for them. Madrid president, Florentino Pérez operates and managed the club so well that they're ranked the best club in Europe all these years. Real Madrid have effective scouting sector that directly offers bids for these rare gems in football.
No I think what really comes into play here is the fact that Alexander Arnold's contract is about to expire and he is a world class RB that would perfectly fit into the Real Madrid game. These high speed, high precision players is what played an important role for Real Madrid for a very long time now and Real Madrid loves RB and LB players to have goal scoring qualities. For quite a while, David Alaba was the one to take the free kicks for Real Madrid, but he is not part of the team at the moment. 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.