The original-round tender will cost them $2.133 million for the 2020 season and give them the opportunity to match any offer he receives from another team.
Redmond, 25, signed with the Bengals in 2016 as an undrafted free agent out of UCLA. He did not make the final roster, but the Bengals signed him to the practice squad for the season.
Redmond was re-signed by the Bengals on a futures deal for the 2017 season and returned to Cincinnati as an exclusive rights free agent last year.
In 2019, Redmond appeared in three games for the Bengals, making two starts.