The England international has started just four LaLiga matches this season, raising questions about his long-term place in Madrid's plans. His transfer from Liverpool was high-profile, but it has so far failed to deliver the impact expected by either the player or his new club.
Liverpool, Arsenal, Chelsea and Bayern Munich are among the sides believed to be keeping an eye on developments. Manchester City would also be interested in the situation, although their own uncertainty surrounding the Premier League charges against the club makes any potential move more complicated.
There is some speculation that Alexander-Arnold will leave in January, but sources indicate that the more realistic opportunity for a transfer would come at the end of the season.
Much will depend on whether he can establish a more prominent role in the weeks and months ahead, but there is a growing sense that a change could become necessary if his situation does not improve.
Chelsea are an interesting possibility as they have an appetite for adding players with Alexander-Arnold's technical qualities, while their updated recruitment strategy could make room for a player of his profile.
Arsenal and Bayern Munich are also clubs worth watching, although a return to Liverpool would seem a particularly complicated proposition given the circumstances surrounding his departure.
Alexander-Arnold has generally enjoyed his life in Madrid, but that does not necessarily mean he will be prepared to accept a reduced role indefinitely.
His exit from Liverpool was controversial, with supporters making their disappointment clear during his final appearances, and a return would carry its own emotional and practical complications.
For now, his immediate priority is to force his way into the starting picture.
His return to the England squad offers some encouragement after being overlooked for the World Cup, but the bigger question remains whether he can convince Madrid that he deserves a central role in their plans.