Williams told USA Today that he hadn't previously heard any interest from New England, so it's quite possible that his public plea led to this visit. It's a perfect fit for both sides. The Patriots love to sign quality veterans looking for a ring. The team also needs depth and bulk on their defensive line. The Pats are too shallow at defensive tackle, especially if Tommy Kelly and Vince Wilfork can't regain their previous form.
The Patriots might not offer Williams a big contract, but they would present another chance for a career that included a lot of losses in Minnesota.