According to Spanish outlet Marca, Real Madrid are keen on signing the 22-year-old and are considering activating his €58 million release clause.
Williams had the clause inserted into the contract he signed last summer and is widely expected to leave Athletic club.
The winger was a key target for Barcelona last summer but ultimately stayed in Bilbao and the newly crowned La Liga champions have since cooled their interest.
Club president Joan Laporta told TV3: "He was one of the candidates last summer, we were evaluating Olmo and Nico. We have a good profile of this player, who is an excellent player, but I think at this moment we are evaluating other options."
Premier League sides Arsenal and Chelsea have also been heavily linked with a move for Williams.