Why would you trade Gibson?
They will not have the cap space to do the options they foresee for themselves at power forward. Even if they amnesty Booze this summer, they will be short cap space for Mirotic, which now they see will cost them much more than a MLE. And if not Mirotic than they will need Gibson's 8 mil in cap space to pursue 2015 FA's namely Kevin Love.
As when they drafted Gibson, they had Tyrus Thomas sitting on cap space and moved him for the Charlotte pick. Now they will use the Charlotte pick to get off the 8mil Gibson is sitting on. The problem is the prospects they are high on are most likely gone before Charlotte's 16th selection. They like a half dozen top draft prospects including (Julius Randle of KY, Aaron Gordon of Arizona & Doug McDermotte of Creighton) The front office would like to have one of them at PF to develop for a year and than play along side Nikola Mirotic or as insurance if he stays in Spain.
They don't have any plans to have Gibson as sole starter at power forward, this has angered Gibson's camp and even Gibson has shown displeasure with his role as bench mob captain. So again the Bulls foresee two futures one with Mirotic at pf and one without. However, both situations don't include Gibson. Without Mirotic they will chase after Love which they will need the cap space. With Mirotic they will also need more cap space and foresee getting a pf on the cheap like currently with Nas at center, or previously with Hakeem Warrick in Tyrus situation.
Their two trade assets are Taj and Jimmy. Although, Jimmy is still on his rookie deal and without moving out a large chuck of salary they will most likely lose him as well. So they would like to move Gibson this summer for a top draft choice. Several teams in Top 10 (Detroit, Boston, Los Angeles, Sac) have interest in trading back to 16 if they can receive Gibson in return. By moving Gibson they feel they can stay productive at the position while getting younger, cheaper and with a higher ceiling.