NFL Network's Ian Rapoport echoed that report, tweeting Sunday evening that "there is not a lot of optimism surrounding the injury."
More will be known after Williams undergoes more tests Monday.
With Williams sidelined, the Broncos will turn to Melvin Gordon and Mike Boone. Denver also has Devine Ozigbo available on the practice squad.
Elsewhere on the injury front, Broncos pass rusher Randy Gregory also suffered a knee injury on Sunday, but he said "I'm good" after the game. The outside linebacker will undergo more testing on Monday, but his comment seems like a positive early sign.
Denver has a short week before a Thursday Night Football showdown with the Indianapolis Colts, so Gregory might be unlikely to play in Week 5 even if he's not expected to have an extended absence like Williams.
Story originally appeared on Broncos Wire