Redmond struggled at times during his first full season as a starter. He was penalized 11 times, the second-highest number on the team behind right tackle Bobby Hart.
The Bengals sought to improve the position in free agency by signing guard John Miller, noting at the NFL owners meetings that they considered him a starter.
A source told ESPN NFL Insider Adam Schefter that Redmond played part of last season with a torn labrum and a hamstring injury, leading to the decision to take a banned substance.
Redmond was not present at the Bengals' OTA practice session open to the media on Monday.
Redmond first showed up on the 2018 injury report on Oct. 3 with a shoulder issue, and then again the week of Nov. 7 with a hamstring issue that led to him missing the Bengals' game against the Saints. Trey Hopkins, the primary starting right guard in 2017, started in his place.
Redmond, 24, was a 2016 undrafted college free-agent signing for the Bengals out of UCLA. Redmond was initially on the Bengals' practice squad before eventually earning a starting role last summer.