Valles, 26, is under contract with Las Palmas until the summer of 2025.
Club president Miguel Angel Ramirez confirmed yesterday that the goalkeeper has decided to move on this summer.
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Relevo says Valles could end up in England.
Arsenal, currently Premier League leaders, are showing an interest in the 26-year-old. But Aston Villa also are keen on Valles.
In Spain, Real Betis are said to have expressed interest in the goalkeeper earlier this year.