NFL.com analysts Chris Wesseling and Gregg Rosenthal have ranked the league's top 101 players who are set to become unrestricted free agents March 11.
Byrd is the only difference-maker in the rankings, which also include 23 impact starters, 37 starters with questions and 50 players who would be effective in the right role.
Three Bears are on the list: Defensive tackle Henry Melton at No. 17, cornerback Charles Tillman at No. 72 and quarterback Josh McCown at No. 76.
The two analysts write that Melton could have been No. 1 on the list a year ago before he sustained a torn ACL last Sept. 22 in Pittsburgh, "so why not swing for the fences for a young player that has displayed top-five talent at his position?"
Wesseling and Rosenthal write that Tillman "was alternately injured and ineffective one season after joining the discussion for Defensive Player of the Year" and that McCown "would make for a much more attractive stopgap option" if he could bring Bears coach Marc Trestman with him.