As of now, the reports are that Portland will not take JJ from the Bulls and are looking for a player like Taj Gibson.  However, I am not willing to give up Taj at this point for Rudy as we would not have a backup PF and there are not great ones on the market.  To get this to happen I tried to think of moves/trades that all teams would appreciate.  Here they are below:

Trade 1: Taj Gibson for Rudy Fernandez

Reason - If this is what it takes to get Rudy I would only do it if the Bulls knew they could get backup PF.  Also, this would be my last option.  I'd first try JJ or charlotte's 1st rounder for Rudy. 

Trade 2: Bulls 1st Rounder for Ryan Anderson (Orlando)

Reason - Orlando is WAAAYY over the luxury tax and already have a backup PF in Brandon Bass.  Otis smith already stated he was looking for trades to relieve some CAP pressure when they resigned JJ.  Ryan Anderson could spread the floor for Derrick Rose as he is a 3 point shooter avg .370 last year and shot over 200 threes.  The Bulls first rounder is likely going to be a top 20 pick next season anyways and will not have much value. 

Trade 3: James Johnson for Jordan Hill (Houston)

Reason - Same situation here for Houston.  They are over the luxury tax and already have big men in Scola, Miller, Yao, Chuck Hayes.  They would save 4 million dollars by this deal given the luxury tax.  I don't know much about Jordan Hill but he was the 8th overall pick and didn't seem to get a good opportunity last season. 

Bulls roster after these moves:

PG: Rose, Watson

SG: Brewer, Fernandez

SG: Deng, Korver

PF: Boozer, Anderson, Hill

C: Noah, Asik, Thomas