Byrd caught one pass for four yards in the Bears' 41-15 preseason loss to the Bills on Saturday.
Byrd was on the field at times with the first-team offense while Allen Robinson was sitting out, but with Andy Dalton unable to move the chains with any consistency, there weren't many targets to go around. Byrd is competing for a role as the team's No. 3 wide receiver as he comes off a career-high 604 yards with the Patriots last year.