Goal says the youngster has a £42.9m release clause which the Gunners may be ready to meet.
Williams, whose brother Inaki is a Ghana international, featured in all three of Spain's World Cup group games.
The 20-year-old only made his senior international debut this year, and scored his first goal for La Roja in a warm-up friendly against Jordan.
The youngster is under contract with Athletic Bilbao until 2024, and Arsenal could face competition for his signature. Chelsea, Liverpool and Paris Saint-Germain are also reportedly keen on a man who scored in three successive games earlier this term.