Other teams reportedly believe McKinley - who has been held out of practice the last two days due to a groin injury - will be moved before next Tuesday's deadline, but no deal is apparently imminent.
Atlanta will hold McKinley out of Thursday's game against the Carolina Panthers so he can heal, sources told Jeremy Fowler of ESPN. However, listing him as inactive could help the team move McKinley, Fowler notes.
The Falcons are apparent sellers after starting 1-6. They also fired head coach Dan Quinn and general manager Thomas Dimitroff earlier this season.
Atlanta selected McKinley with the 26th overall pick of the 2017 NFL Draft.
The young defensive end racked up 13 sacks and two forced fumbles during his first two seasons. However, he struggled in Year 3 and produced only three quarterback takedowns. McKinley has one sack so far in 2020.