But it's some other former Tennessee products that Williams is hoping to emulate, namely John Henderson and Albert Haynesworth.
Both became first-round picks in the draft and both went on to make the Pro Bowl.
"We have guys that come out every year," Williams said at the scouting combine. "That is part of the reason I went to Tennessee, for the great tradition of defensive tackles. When I first got there, Coach Dan Brooks is a great coach and I think he still is producing good products. … The prestige of defensive tackles at Tennessee, it's a long list. One of my goals in going to Tennessee was to add my name to that list."
To say Williams was a "prestigious" defensive tackle at Tennessee might be stretching the truth, but by his senior season he had become a bona fide first-round prospect.
It was quite a move up for someone who was considered "just a guy" following his junior season in 2008.
There were several factors involved in Williams' drastic improvement. One of them was a talk last summer with Haynesworth, who passed along some tips. Another was the chance to play one year under former Tampa Bay Bucs defensive coordinator Monte Kiffin, who had joined his son Lane's coaching staff with the Volunteers.
Whatever the reason, Williams went from 48 tackles as a junior to 70 as a senior, and that was good enough to earn him second-team All-SEC honors from both The Associated Press and the league's coaches.
Williams then had a productive week at the Senior Bowl, where he played on the South team coached by Tony Sparano.
All the while, Williams' draft stock went up. Not that he's paying too much attention.
"The only thing I can control is what Dan Williams does," he said. "I can't control who ranks who higher or who says who's better."
Williams shouldn't feel bad, though, because Suh and McCoy are ranked among the top prospects in the draft at any position.
Nonetheless, Williams says the two Big 12 stars have nothing on him.
"If you want to say who is better, you can put Dan Williams' film against anybody's film," he said. "Look at Suh and McCoy and you tell me who is better. That is my resume and that is what I can go by."
Helping Williams' stock -- and what makes him attractive to the Dolphins -- is the fact he can line up at nose tackle as well as playing tackle in a 4-3.
And for a nose tackle, he showed some good pass-rushing skills last season.
"That was an area I was working on in the spring and summer and that's the part of the game I always said I was going to improve on," Williams said. "I guess this year it kind of showed up; it might not have shown up in sacks but if you watch film you will see more pressures and hurries and the quarterback got rid of it right before I got there. I worked on it every day to try and improve and I think my work paid off."
You could say the same for every part of his game.