The Bulls have the rights to the best player in Europe (Nikola Mirotic), who will in all likelihood join them next year. They have two firsts (#16 and #19). There is no reason for them to break anything up, aside from amnestying Boozer to create $17 million in cap room.
Wow...so they could presumably just give Boozer the boot and then use that money to sign Melo if he opts out of NY, right?
They'd have to make some sort of additional cap clearing move to pull off signing him outright, since Mirotic will probably take up about $5-6 million of that cap space. Probably they'd have to move Taj Gibson (who also plays the 4 like Mirotic). Likely the only way they end up with Melo is convincing NY to take Boozer back as an expiring, or convincing a third team to take him on.
I believe if they amnesty Boozer they can start a contract offer to Melo between 15-16 million. So Melo would have to take a pay cut, but not a gigantic one. They wouldn't be able to bring Mirotic over though, but with Melo they wouldn't need Mirotic and they could move him for other pieces.
A few things:
1) Melo currently makes over $21 million -- his max deal next year is near $22.5 million, if he gets max. $15-16 million is a pretty big pay cut. I just don't see him willing to do that. Maybe $19-20 million, but $15-16 is too low.
2) If they amnesty Boozer for cap space, they have to use some of that space on Mirotic, and it will likely have to be around $6 million so that he can be paid a large enough signing bonus to get out of his buyout with Madrid.
3) If they amnesty Boozer, they'll have $17 million of cap space, but only have 6 players under contract, which means they have $3 million in cap holds, taking them down to $14 million. They also have, as noted, two first rounders, who will take up about $3 million with their cap holds. Now maybe they'll draft a Europlayer for a draft-and-stash, but it's still trimming from their cap.
Point is, I don't see how they make enough room for Melo, much less Melo and Mirotic, without trading away some sort of additional, probably significant salary. I do think Melo can land there, however, in some 3-way trade similar to the Iggy sign-and-trade from last summer, with Boozer as the main piece of salary. They could then preserve the mid-level exception to sign Mirotic.