It remains to be seen whether moving on from Gordon will prompt the Browns to revisit contract talks with free-agent receiver Dez Bryant.
Gordon was ruled out for the Saints game on Saturday due to a hamstring injury despite no mention of the issue on the injury report during the week.
Gordon was healthy for and during Friday's practice, usually when teams start to make final decisions on roster counts for Sunday's matchups. The team's medical staff examined Gordon and determined he shouldn't face Saints, but there was also a sense within the organization Gordon could be struggling again with his battle with drug and alcohol addiction.
Gordon, who has dealt with substance abuse problems for most of his career, missed training camp as he sought mental health treatment but made his return ahead of the season opener.
Josh Gordon received countless chances the past six years from the Browns until the franchise finally reached the point where it felt it could no longer stick with the ultra-talented, troubled receiver.
Kirksey, who had been listed as questionable, will miss his first game after playing in 65 straight since being drafted third round in 2014.
The 27-year-old caught a game-tying, 17-yard touchdown pass in the fourth quarter against the Steelers, but Gordon was mostly used as a decoy.
Jackson refused to elaborate on the situation this week, saying he and the coaching staff wanted to "move on".