Williams has had a transfer request rejected, and Barnsley's undisclosed bid was dismissed by the Iron.
The wantaway left-back has turned down the offer of a new contract at Glanford Park, but has 12 months left to run on his current deal.
United were reported to be considering a swap deal involving Tykes full-back Robbie Williams, but boss Nigel Adkins has denied his interest in the left-sided defender.
The 22-year-old has since turned down a new deal at Oakwell and remains with Barnsley on a week-to-week contract.