So where will the six-year pro end up playing?
Don't count out the Atlanta Falcons, we keep hearing, as do some team officials around the league.
Let's call it, for lack of a better term, a semi-educated guess.
Maybe for some it's nothing more than an exercise in connecting the dots, always a dicey pursuit in the free agent game, but the Falcons have a need for a pass-rusher.
And, while Williams will have his share of suitors, expect the Falcons to be in the hunt.
Owner Arthur Blank certainly has a history of making free agent splashes, the team plays Williams' preferred front, a 4-3, and Atlanta might be emboldened some by the current problems confronting arch rival New Orleans, and try to steal the NFC West.
New defensive coordinator Mike Nolan could use Williams in a variety of ways in an attempt to create pressure on the pocket.
Williams is going to command a ton of money, but Blank, obsessed with winning a Super Bowl, has never been shy about pursuing high profile veteran players.
Witness the free agency signings of tailback Michael Turner (six years, $34.5 million in 2008), cornerback Dunta Robinson (six years, $57 million in 2010) and defensive end Ray Edwards (five years, $30 million in 2011). Robinson and Edwards so far have provided pretty disappointing returns on the investments, but that probably won't be enough to dissuade Blank from chasing Williams, if his personnel people target him.
Plus, the Falcons are leery about laying out too much to retain end John Abraham, their lone legitimate pass rusher, but also 34 years old.
The Falcons may not land Williams, who is said to be somewhat enamored of the Falcons' possibility, but it's a pretty good bet they'll be interested.
Said one team official whose team is also expected to pursue Williams: "(Blank) is a hell of a closer. And he isn't afraid to spend."
NFL Free Agent Rankings
Free Agency News
Hot Topic: Will Moss Return To New England?
Len Pasquarelli is a Senior NFL Writer for The Sports Xchange. He has covered the NFL for 33 years and is a member of the Pro Football Hall of Fame selection committee. His NFL coverage earned recognition as the winner of the McCann Award for distinguished reporting in 2008.
For more Patriots news follow us via Twitter: Follow @patriotsinsider
Or find us on Facebook : Facebook.com/PatriotsInsider