McKinley, the 26th pick in the 2017 NFL Draft, recently said he asked for a trade the past two seasons and took to Twitter to voice his displeasure with the Falcons' failure to find a trade partner at this year's deadline.
After McKinley's public criticism, interim head coach Raheem Morris said the Falcons had to figure out "if he can even be on this team."
McKinley has appeared in four games this season and missed time with a groin injury. He has just one sack this campaign after racking up 16.5 total sacks in his first three seasons.
The 25-year-old was playing in the final year of his rookie contract. The Falcons declined the fifth-year option in his deal prior to the season.