However, the offer from the Shrews’ League One rivals for the 22-year-old defender has been called ‘derisory’ by Williams.
Williams, who earlier this week spoke of interest from Leeds in the club’s star player, insists Shrewsbury will not be selling their assets on the cheap.
He told the Shropshire Star: “To say that the offer from Swindon was derisory is an understatement, and it was rejected forthwith.
“I had to check the calendar to see that it wasn’t April Fool’s Day. In fact, if it had have been April 1 we’d have all fallen for it because I thought it was someone winding me up.
“We thank Swindon for their offer and wish them well in their recruitment for the summer and look forward to seeing them in December. But if they think Shrewsbury Town is a small club with no ambition that will sell their prized assets on the cheap, then they’re sadly mistaken.
“We’re looking forwards, not backwards. Yes, finances are tight but we’re a well-run club with no debt and we will not sell our best players for less than they’re worth.”
Goldson, player of the year last season at Greenhous Meadow, made 51 appearances in all competitions for the Shrews during the 2014/15 campaign.