The 33-year-old Williams is a six-time Pro Bowler who has been extremely durable over his career, missing just five regular-season games since entering the NFL as a first-round draft choice out of Oklahoma State. At 6-foot-5 and 311 pounds, he has been a solid interior rusher, with 60 career sacks.
Williams has previously visited with the Seahawks and Giants. His former position coach in Minnesota, Brendan Daly, is in his first year on the Patriots' staff.
USA Today's Tom Pelissero interviewed Williams earlier this week, and Williams said he'd consider retirement but, "I hope to be on somebody’s team before summer’s out."