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With Texans running back Arian Foster now signed to a new five-year deal, the question becomes whether the team will use the franchise tag on linebacker Mario Williams.

Given that the final year of Williams’ rookie deal had a cap number that would push his franchise tender above $22 million, that’s highly unlikely.

Making it even more highly unlikely is the fact that the Texans and Williams have yet to engage in serious negotiations, according to a source with knowledge of the situation.

As of last Tuesday, the Texans had $118.9 in 2012 salary-cap commitments, which puts them close to the expected ceiling of $120 million or so. Foster wasn’t factored into the “top 51” calculation, since he wasn’t under contract at the time. His cap number for 2012 will land on the “top 51” list, nudging a minimum-salary guy off the board and taking more dollars away from the team’s allotment.

The Texans could tag Williams by 4:00 p.m. ET Monday, adding $22 million to their cap commitments. The team then would have to embark on a one-week effort to clear cap space. Candidates for restructured deals and/or pay cuts include receiver Jacoby Jones ($3 million base salary in 2012), linebacker DeMeco Ryans ($5.9 million), quarterback Matt Schaub ($7.15 million), receiver Kevin Walter ($3.5 million), and tackle Eric Winston ($5.5 million).

There are three other reasons to not keep Williams. First, in a 3-4 defense, outside linebackers can be capably filled by a much less expensive player. For years, the Steelers had a revolving door at the position, letting “star” players walk and reloading with guys who had the ability to take advantage of a potent three-man defensive line that ties up the blockers. The Texans will have a hard time justifying the extra money it will take to have an elite player like Williams in that role.

Second, the team performed very well without Williams, who missed most of the season after tearing a pectoral muscle.

Third, the Texans need to keep those big dollars around in the event that they decide to make a run at Peyton Manning. They reportedly aren’t interested — but at one point the Vikings reportedly weren’t interested in Brett Favre, either. With Schaub entering the final year of his contract, the Texans could clear a quick and easy $7.15 million in cap space by cutting him loose.

And the Texans, who spent nine years unable to get to the postseason due in large part to Peyton, would suddenly become a championship contender if the guy who was throwing passes at Duke on Friday ends up throwing passes in Houston.