12/15 is an important CBA date, as nearly all players signed in the offseason are eligible to be traded. For the Bulls, it's literally everyone, including Kirk Hinrich, Marco Belinelli, Nate Robinson, Nazr Mohammed, and Vlad Radmanovic.
This means the trade season is unofficially open. Both Marc Stein and Marc Spears (via Nets Daily) have recently put up lengthy columns going through scenarios, and not a single Bull is mentioned in either. I suppose that makes sense: the Bulls are hard-capped, so any trade will have to be at least money-neutral. And we know as an organizational direction they're not really trying to win this year, and are more likely just looking to deal away salary to reduce their luxury tax payment.
They could do some minor roster-reshuffling and gain some improvement, likely through getting some kind of frontcourt depth. However the current injuries to Hinrich and Hamilton (let alone Rose) don't really give them a lot of options at this moment.
All that said, the Trade Machine is great and no Bulls names are grayed out anymore, so (seriously) have fun pretending.