Green has not practiced all week and the Bengals (5-5) said they will reevaluate him on Saturday.
Bengals head coach Marvin Lewis said earlier in the week that although Green had not yet been able to practice, he expected the wide receiver would be on the field sometime this week and that he thought he would play against the Browns.
Lewis said on Friday that he hoped Green could practice on Saturday.
The 6-foot-4, 210-pound Green has 45 receptions this season for 687 yards (a 15.3-yard average) and six touchdowns. He averaged 85.9 receiving yards in the eight games he has played.
Safety Damarious Randall of the Browns (3-6-1) told Nate Ulrich of the Akron Beacon Journal: "If they don't have A.J., they're getting their [butt] beat."
Also on Friday, the Bengals placed defensive tackle Adolphus Washington (knee) on injured reserve and signed defensive tackle Christian Ringo to fill Washington's spot on the roster.