With this huge wheel of free agents spinning, one things strikes me. Neither Wade or LeBron want to be left on a team that can't win a title. The ideal situation is for the Bulls to land Chris Bosh, however, it doesn't seem likely that Bosh is coming here to force the issue. If he did, then one of LeBron or Wade would likely follow suit quickly, but he's not, so they won't.
However, that's where Carlos Boozer steps in.
Say the Bulls sign Boozer today.
Bosh will then play with either Wade or LeBron in Cleveland or Miami. The other guy is then left with what? If Bosh joins LeBron in Miami then Miami's off-season is down to some combination of second tier guys like David Lee, Anthony Morrow, JJ Reddick, and Brendan Haywood. He said he'd leave without getting significant improvements, but significant improvements would clearly not be coming.
If Bosh goes to Miami with Wade the case for LeBron isn't nearly as straight forward. He still may opt to continue to not win titles for his home town, but his odds of winning will continue to fall as his team gets worse and still lacks assets to improve considerably. The Bulls team will then have Rose, Deng, Boozer, and Noah.
Is that enough to lock in LeBron? How badly does he want to win?
The latest rumors are that LeBron is recruiting Bosh to Cleveland heavily and may delay his decision. The implication being that LeBron will stay in Cleveland if Bosh commits (or another considerable talent upgrade), but he won't otherwise. If he would still stay in Cleveland either way then he'd be ready to commit now rather than delaying it.
That seems to imply that a Bosh -> Miami scenario makes it likely that the Bulls come away with LeBron though he'd still perhaps give some consideration to the Knicks with Amare.
Either way, if everyone wants to be left with someone, then Bosh + Wade or LeBron is one pairing, and Boozer / Amare + the other is another. If the Bulls get Boozer then they're left competing against the Knicks for the superstar who's left, and they have a much better situation to sell than New York.