Williamson is well down the pecking order at United, and Alan Pardew has a central defender top of his wanted list.
A bid of around £2m would tempt Newcastle to let him go, and give the player the chance of regular Premier League action with the newly promoted side.
Mackay previously worked with Williamson at Watford.
The only problem seems to be the wages, as the 29-year-old is said to be on £40,000 per week, and he would have to take a pay cut to make the deal work.
Source: Newcastle United Mad