I expect the Pats to pursue this guy and have a fair shot of signing him. BB has a history of being involved when marque players at this position become available (see Colvin, Thomas, Peppers). Colvin was a good player during his time, and would have most likely been a star if not for a freak hip injury. Thomas was a good player whose Raven mentality eventually surfaced by the end. The Bears made a ridiculous offer to Peppers that the Pats would not match. BB isn't afraid to open the wallet for players that can be staples on his team (Colvin, Thomas, Wilfork, Mayo).
It's rare that a player of Williams' caliber and age hits the market. You can instantly plug him in and build a defense around his demonstrated flexibility (has played in both 3-4 and 4-3 successfully). From all accounts, he seems to be a good guy who can buy into the Pats philosophy. He's already made a ton of money as well (65mm or so over rookie contract), which means he may be willing to consider intangible factors (opportunity to be on a consistent winner) rather than just pursuing the highest dollar. Given that his team made the playoffs for the first time this year, and he wasn't able to participate (being injured), he may be attracted to the Pats' model of consistency.
Also, as we have seen with other DE/OLB players that the Pats have talked to, BB has a way of getting them excited when discussing the different ways that he plans to use them in the Pats' defense.