White appeared to tweak his ankle in last Sunday's 26-24 loss to Cleveland, but he remained in the game. He also has battled knee and hamstring issues this season.
Soliai's absence was not injury related. He's not expected back on Thursday.
Offensive tackle Jonathan Scott, who had been sidelined with a hamstring injury, was on the field but limited.
Cornerback Robert McClain, who suffered a calf injury against the Browns while starting in place of Alford, did not show up on the injury report.