The Bengals chose Williams with the No. 11 overall pick in the draft in April and installed him at left tackle in their offseason program.
However, an unidentified injury caused him to miss the end of OTAs.
While Taylor declined to speculate on his condition, a team spokesperson prevented reporters from asking Williams about it, raising concerns the injury might be serious.
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Injuries have become all-too-common for Bengals No. 1 picks recently.
After cornerback William Jackson III missed all of the 2016 season with a torn pec, receiver John Ross III played only three games in his rookie campaign while dealing with multiple ailments, including to a knee and shoulder.
Center Billy Price began last season in the starting lineup but missed six games with a foot injury before returning to finish out the season.