Radio Marca's Ramón Álvarez de Mon is reporting on X that Alexander-Arnold has approved the move.
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The England international is off contract in June and will be free to sign pre-contract terms with Real from January 1. However, it's suggested a January transfer isn't off the table.
De Mon has stated: "Arnold has said yes to Real Madrid. There is a full agreement for his free arrival in 2025, although obviously nothing has been signed.
"The possibility of bringing the signature forward to January is not excluded, but it is complicated."