Chelsea have long been interested in the winger, who had an outstanding season with Athletic last season, scoring eight goals and assisting 19 times in 37 games.
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However, Williams agreed to a new, long-term contract with his club (Athletic Bilbao) in December last year, which includes a release clause worth over £49 million.
According to different reports, the fee is too much for Chelsea, who are searching for less expensive options to strengthen its attacking depth out wide.
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While Chelsea has withdrawn from the race, Premier League rivals Arsenal remain keen in pursuing a deal this summer.
Mikel Arteta considers Williams to be one of his top attacking alternatives, but the club is concerned about the high asking price and compensation necessary to pull him away from his childhood club.
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Williams, however, denied speculations of a possible transfer last week, insisting he was ‘happy’ at Athletic Bilbao.
‘I have read stories concerning my future, but I honestly do not know anything,’ he stated.
