At 44 years of age, Williams accepted the advances of McAllister despite an advantage of over 100 pounds on their last scaling.
McAllister, 35, is obviously planning on piling the weight on for the July 28 contest, although Williams is sure he can end the fight early.
“Lee McAllister was a really good lightweight and I have watched some of his fights in the past. He is a good fighter,” Williams told the Aberdeen Evening Express.
“However, he is a former lightweight and now wants to fight at heavyweight – I’m shocked.
“There is a reason we have weight divisions in boxing and I would show McAllister he should keep himself down to the lower weights.
“If he was to come up against me I would win easy, maybe a three-round win.
“McAllister has good footwork and has probably still got it but I would definitely see him off,” he added.
Williams is most famous for his stoppage of a knackered Mike Tyson in 2004 and having a record of 23-23 over his last 46 contests.
Taking on the likes of McAllister is certainly a publicity stunt, which fans will have to take as they see it come fight night at the Aberdeen Beach Ballroom.