Free agency officially starts at 4 p.m. ET on Tuesday. The Texans declined to apply the franchise tag to Williams, which is valued at $10.605 million for 2012.
Williams, the first pick in the 2006 NFL Draft, suffered a season-ending torn pectoral muscle in Week 5 last season. While the Texans' defense continued to play well after losing Williams, the 27-year-old is considered the top defensive free agent this offseason after totaling 53 sacks in his first six seasons.
Elite pass rushers are at a premium on the free-agent market, and offers from elsewhere are another concern for the Texans.
The Chargers, for one, have reportedly assigned an unknown price that they would be willing to pay to sign Williams, U-T San Diego reported Tuesday. The newspaper also reported the team spoke with Williams' agent, Ben Dogra, at the NFL Scouting Combine last month.