Bulls are actively shopping Ty Thomas and Hinrich is redundant with Rose and Gordon (assuming they re-sign him). Allen is another shooter which the Bulls need especially with Gordon's inconsistency. Rose, Gordon, and Allen would be a great backcourt rotation for the Bulls and with Noah, Deng, Salmons, and Tim Thomas at the 3 and 4, they don't really need Ty Thomas.
Rumor has it they would prefer a PF for the Thomas/Hinrich combo, but I'm not sure they would do better than Ray Allen, who in addition to being a great shooter would provide them the veteran leadership they could really use.
The C's would add an athlete who can play PF and SF and would get a great backup PG that could easily play with Rondo (obvioulsy against bigger SG's it would be problematic, but against most SG's that combo could be deadly with the speed, driving ability, and ball handling).