Williams emerged as a target for United during the closing days of the Premier League transfer window, with Romelu Lukaku heading to Inter.
The 25-year-old Williams, though, remained at Athletic and signed a nine-year extension with a €135million release clause.
Reflecting on the August speculation, the Spain forward said: "I had contact from Manchester United but I cannot tell you who it was.
"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."
Williams made his Athletic debut in 2014 and he has since scored more than 45 goals in all competitions.
The one-cap Spain international enjoyed his best scoring season in LaLiga last term, netting 13 times in 38 matches.
Williams has already scored once this term for Athletic, who are unbeaten after three matches and two points adrift of leaders Atletico Madrid.
Athletic travels to newly promoted Mallorca after the international break on Saturday (AEST).