The semantics are important here. If teams are inquiring about Jimmy and the Bulls are responding with very high asking prices, I don't consider that "shopping", just listening to what the pulse of the league is. I'm sure the Bulls do this, and I'm guessing they have a list of about 15 or so players they'd have to get back in order to make the trade worthwhile. If you can get one of those guys, maybe you blow the whole thing up. But that's very different from actively soliciting teams for deals in an effort to move him.
As long as Butler is coachable enough and doesn't cause trouble for management in the press I don't think they are getting rid of him. They can make the 1st round of the playoffs with Butler as the key cog and that is the main goal for the organization. Some scenarios where they might get rid of Butler? 1.) He starts bad-mouthing management or the coach a lot publicly again. 2.) Management starts feeling some real heat that they might lose their job. Not just Freddie Del Hoiberg and Gar (who was hired to be fired), but Paxson. In this case, I could see perhaps a Butler trade for young players / picks to create a "rebuild" story and preserve paychecks for a few more years.
IF a team has the right assets to trade (young, athletic ballers) AND that team thinks Butler is even better than the Bulls think he is, then I can see Butler being traded. I don't see Butler being traded.
Right. Keeping Jimmy keeps the path forward most closely aligned with the Front Office's MO. Jimmy is good enough right now that he can drag a team of scraps into playoff contention and you can probably build a 50 win team around him using a close-to-the-vest, risk-averse strategy that wouldn't risk dips in TV Ratings or ticket attendance. It'd have to be a pretty remarkable offer to cause the Bulls to trade Jimmy.