Marca says the 22 year-old's deal with Girona runs to 2027 and significantly carries a buyout clause of just €14m.
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Watching Arnau's situation are clubs across Europe, including West Ham, Marseille and Juventus.
Girona coach Michel admitted last week: "The most important player on the team is Arnau Martínez , because of how he plays in attack and defence.
"He's a game-changer."