Summary
Aminu signed a 3-year, $29 million contract with Orlando in 2019, and due to injuries has been unavailable during most of that time. Aminu only played in 18 games in '19-'20 and 23 games this past season. If Aminu were a free agent this summer, I'm not sure he would get any offers above the minimum. He'll be 31 by the time next season rolls around, and with his recent injury history there are no guarantees he can even be available on a consistent basis, let alone actually contribute to winning.

If Aminu can get healthy and put together a solid season in '21-'22, it's possible he could get one last decent contract. It's not long ago that Aminu was starting for a successful Blazers team as a combo forward that could defend multiple positions. Aminu's lack of shot-making ability hurt him in the playoffs, but he hit enough during the regular season to at least keep defenses somewhat honest. However, I think Aminu is more likely to be out of the league than he is to be a starting level forward like he was in Portland.
 
Cap Considerations
Aminu has a $10.2 million player option for 2021-2022. If Aminu opts out, he will be an unrestricted free agent with a $18.5 million cap hold and Early Bird rights.  Since his cap hold is above his market value, his cap hold really isn't that relevant, as the Bulls will either let him walk in order to maximize their cap space, or they will re-sign Aminu and cut into some of their space. The Bulls also may end up operating over the salary cap. The Bulls could offer Aminu a starting salary of up to $17 million using the Early Bird exception, which is more than enough even in the unlikely scenario Aminu opts out.

Other teams will have multiple ways to sign Aminu as even teams without cap space could possibly use either of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE to sign him. I'm not even sure Aminu would get more than the minimum if he were to opt out.