Alexander-Arnold joined Madrid from Liverpool in 2025 after his contract at Anfield expired, with the Spanish club paying €10m to bring him in early for the Club World Cup.
The England international provided seven assists in 35 appearances during his debut season, starting 27 of those matches.
However, his involvement has fallen this season. Alexander-Arnold has started only two of Real Madrid's opening seven league matches, with two further appearances coming from the bench.
Liverpool have previously explored the possibility of bringing their former academy graduate back to Anfield, although Madrid were unwilling to consider a sale.
That situation could change if Alexander-Arnold's lack of regular football continues.
According to Fussball News, Arsenal are now seriously considering making an approach for the 27-year-old.
Mikel Arteta already has Jurrien Timber and Ben White capable of playing at right-back, but Alexander-Arnold's attacking qualities could tempt Arsenal to strengthen the position.
His ability on the ball and particularly his right foot are reportedly among the qualities that appeal to Arteta.
Real Madrid are said to be prepared to consider selling Alexander-Arnold if they receive an offer in the region of €70m-€80m.
The defender therefore faces an uncertain situation at the Bernabeu, with his future potentially dependent on whether his role increases during the season.