Beckham will not practice because of a non-injury-related personal matter, according to the team.
On Tuesday, Odell Beckham Sr. posted a video on Instagram highlighting times when Mayfield didn't throw the ball to Beckham when he was open. Beckham Sr. responded with three green check marks in the comments section of a post that said Mayfield was "either hating on Odell or he just doesn't want him shining." Beckham Sr. also responded with "#bigfacts" to a post that called Mayfield "mediocre."
Mayfield, whose normal Wednesday media availability was postponed, has yet to comment.
Beckham had one catch for 6 yards in Sunday's 15-10 loss to the Pittsburgh Steelers. Mayfield targeted Beckham again late in the game, but the wide receiver went up for the ball with only one arm and failed to come down with the catch.
Cleveland's passing game has struggled in recent weeks, as the Browns have fallen to 4-4. Mayfield ranks 27th in QBR (42.2) and has only six touchdown passes. Beckham, meanwhile, ranks 151st in the NFL in receptions per target and 139th in receptions per route run.
Both players have played through shoulder injuries this season.
The Browns discussed a trade of Beckham with the New Orleans Saints, according to ESPN's Kimberley Martin, but no deal was reached by Tuesday's deadline.
Beckham is under contract for two more seasons but has no guaranteed money left on his deal. He has a $1 million roster bonus due on the first day of training camp each of those seasons. The Browns would save $15 million on their salary cap if they were to trade or release him during the offseason.