The Basque-based player is one of many who United are targeting in the summer.
Per Sport, United are joined by Chelsea and Liverpool in wanting to sign the speedy winger.
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Williams is only 21 and is the younger brother of Athletic teammate Inaki Williams.
While he would prefer to stay in his homeland for the coming years, he may choose to move out of sporting ambition.
Athletic Club did win the Copa del Rey this season, but are not seen as contenders for La Liga or a European trophy.