The Bulls free agency period got officially moving yesterday with news of the craptain's bloated option being picked up and the Maximum Qualifying Offer being extended to Jimmy Butler.
With Jimmy likely getting a maximum deal (at least for 3 years) and Hinrich still on the books, the Bulls have some avenues to add players still while encroaching into luxury tax. Though you could take Gar Forman's proclamation of them being a tax team as "unfortunately we're in the tax so we can't do much" instead of "we're going to be in the tax regardless, so might as well do what we can."
To that end, a lot will be indicated with the decision to retain Mike Dunleavy or not. The Bulls are speaking positively, and have no reason not to. They also can offer likely more than any other team would, as their early-bird rights on Dunleavy is near the full-MLE and far above the taxpayer-MLE. The latter is what teams like Cleveland (and their GM has interest) or the Clippers could offer.
I'm still skeptical they are that genuine in their proclamations for Dunleavy's return, not just due to the money but that he is going to be 35 next season and effectively blocking their two recent draftees at that same position. Part of the reason Thibodeau was let go was a lack of minutes for Doug McDermott and Tony Snell, and I can only assume that they feel they nailed both picks and both will break out this season.
If the Bulls are serious about adding to the payroll, they'll also have their own Taxpayer-MLE (~$3.4m) to use on someone who is commanding more than the minimum. You'd have to think that will go to someone who can handle the ball, as though they're already paying nearly $3m to a backup PG in Hinrich, we all know that's not sufficient.
Some names that have cropped up to that end, from the invaluable HoopsRumors: