With the lack of moves lately in free agency from the Bears, we can expect a little "rebuild" next season. This does not totally rule out any chance for the Bears the make the playoffs, especially in a weaker NFC North division and with a very favourable schedule. However, this means that Ryan Poles will try to have a roster filled with young, promising players.
I think if the Bears were able to get the same kind of compensation that they received for fellow edge rusher Khalil Mack, they would do it. Let me remind you that the Bears got a 2nd and a 6th round pick for Mack. However, with Quinn being 31 years old, I don't think this is plausible.
With that being said, barring unforeseen circumstances, I think Quinn will be playing in a Bears uniform in September 2022.