Per ESPN's Josina Anderson, one Browns source said they are "not certain" Bryant still wants to play football anymore.
Bryant met with the Browns last month, but the two sides separated without reaching an agreement.
Per Pro Football Talk's Mike Florio, Cleveland's offer to the three-time Pro Bowl wide receiver included less than $5 million in base salary.
The Browns figure to be in the market for a receiver yet again after the team announced that Josh Gordon will be released on Monday.
"This afternoon we informed Josh Gordon and his representatives that we are going to release him on Monday," Browns general manager John Dorsey said. "For the past six years, the Browns have fully supported and invested in Josh, both personally and professionally and wanted the best for him, but unfortunately we've reached a point where we feel it's best to part ways and move forward. We wish Josh well."
Bryant, 29, has been a free agent since being released by the Dallas Cowboys in April. Per NFL reporter Ed Werder, the 2014 All-Pro turned down a multiyear offer from the Baltimore Ravens because he was seeking a one-year deal that would allow him to hit the market again in 2019.