The ball appeared to clearly be in Williams' court as the Bills expressed a desire to re-sign the five-time Pro Bowl defensive tackle as recently as the National Football League combine earlier this month.
Williams, 34, will enter his 13th season in Buffalo after being selected in the fifth round of the 2006 draft.
Speaking of the Chiefs, they were reportedly among the interested parties for Lotulelei, the former Carolina Panthers defensive lineman who would have helped fill a significant hole along the line in K.C. Bennie Logan is now a free agent, as is Jarvis Jenkins, and there has been zero buzz concerning either player returning to this point.
After the Bills' wild-card playoff loss to the Jacksonville Jaguars, Williams said he would take time this offseason before deciding his playing future.
In his career, he has started 75 of 76 games, with 88 tackles, 11.5 sacks, two forced fumbles and two fumble recoveries.
Lotulelei's addition is the latest bold move made by Beane in reshaping Buffalo's roster since being hired in May to replace Doug Whaley.
The Bills had created more than $15 million in salary-cap space in trading away QB Tyrod Taylor and left tackle Cordy Glenn in recent days.
The deals continued strengthening Buffalo's bid to consider selecting one of several highly regarded quarterback prospects in the first round of the draft next month.
Lotulelei, 28, is a former first-round pick and Pro Bowl selection.
The overhaul comes despite the Bills coming off a 9-7 season in which they ended a 17-season playoff drought.