With their backfield facing a plethora of questions following off-field incidents this offseason, the Buffalo Bills are looking to add a veteran.
The Bills put out an offer to Bush, but the running back is weighing his options and is in no rush to make decision, added Rapoport.
Williams' four-game suspension was announced on Friday. Rookie running back Jonathan Williams was arrested on suspicion of driving while intoxicated last week -- while he could be subject to the personal conduct policy, those cases generally aren't resolved until the subsequent season.
Bush, 31, would add insurance behind starter LeSean McCoy while the team waits out Williams' suspension. Bush played in just five games in 2015 before suffering a season-ending knee injury. Bush's injury history is a concern in itself. In 10 NFL seasons, the veteran has played a full 16-game slate twice.