Matt Bowen's recent story at National Football Post doesn't disclose an obvious suitor for Mario Williams, other than it appears that the Texans won't re-sign him. They have some good, young outside pass rushers, and apparently the budget busting value of Williams's contract doesn't appeal to them.
His situation reminds me a little of the one between the Green Bay Packers and Aaron Kampman. Just as Williams was asked to do last season, Kampman was asked to move from DE to LB when the defense made the switch to a 3-4 scheme. For both players, their seasons ended with an injury, and (apparently) neither was re-signed in the offseason.
But there are a couple of differences. First, Williams is younger (he just turned 27) and he should have a couple more prime seasons remaining. Second, while Kampman never seemed comfortable with the switch, Williams played pretty well as a linebacker. It was assumed that Kampman would sign with a team in a 4-3 scheme, while Williams can sign with either, which has to improve his value.
If the Bears really want to make a big splash in free agency, outside of signing one of the premier WRs available like Marques Colston or Vincent Jackson, Williams would be the best player available. But the Bears pass rush is pretty good already, and a big signing on defense wouldn't bring as much value to their team as a wide receiver.