The pacey forward was linked with a move to Old Trafford during pre-season as Ole Gunnar Solskjaer looked to bolster his squad ahead of the new campaign.
And Williams has revealed that the Red Devils did enquire as to whether he would be interested in moving to the Premier League, but he instead opted to remain in Bilbao.
"I had contact from Manchester United but I cannot tell you who it was," he told radio station Cadena SER.
The 25-year-old signed a new nine-year deal with Athletic in August, which saw his release clause increase from €85 million (£81m/$95m) to €135m (£125m/$150m).
Having come through the club's academy, Williams has made 207 appearances for the San Mames outfit since his debut in 2014, scoring 50 goals.
But he insists he is going nowhere, and even suggested that he could look to retire with Athletic when the time comes for him to hang up his boots.
"My number one option has always been to stay at Athletic Club and to retire here. Joining Real Sociedad? No, I could never go there. 100 per cent."
Athletic sit second in the Liga table following their first three matches of the season having picked up two victories and a draw.
Williams then got off the mark for the season with the opening goal of his side's 2-0 victory over Sociedad in the Basque derby, leaving Gaizka Garitano's side sitting two points behind early pacesetters Atletico Madrid.
They return to action following the international break on Friday when they visit newly-promoted Real Mallorca.