The 24-year-old is currently with Spain for the Nations League but spoke about his ambitions with his club in an interview with El Desmarque.
Williams remains determined to deliver a trophy that would have particular significance for Athletic, who have never won a major European title.
“We have the thorn in our side from the semi-final against Manchester United. On top of that, everything was looking good for us because the final was in Bilbao, at San Mamés, our stadium.”
“It would have been incredible and I want to win a European title because nobody has won one and we would go down in history,” Williams said.
Athletic's Europa League campaign ended in the semi-finals against Manchester United, denying them the chance to play the final on home soil.
Williams now wants to help the club go one step further and deliver a landmark European success.