The Bulls have long been considered one of the front-runners to steal Anthony away from the Knicks, so it's little surprise that they will get the first crack at him. The Bulls could form their own Big Three with Anthony, Derrick Rose and Joakim Noah, and Anthony also admires head coach Tom Thibodeau. While Chicago won't have maximum cap space for Anthony, they could still open up a good chunk by amnestying Carlos Boozer and moving some other parts. A sign-and-trade for Anthony involving Boozer would be the most ideal scenario, but the Knicks currently have little interest in Boozer.
The fact that the Lakers are receiving a visit shouldn't come as a huge surprise, but a previous report had stated Anthony would not be visiting them in free agency. Things have clearly changed, and the Lakers will have a chance sometime next week to sell Anthony on coming to Los Angeles. The Lakers will likely have the cap space to offer Anthony the max if they so choose.
After visiting the Bulls, Anthony will fly to Texas to meet with the Houston Rockets and Dallas Mavericks on Wednesday, with the Rockets first on the docket. Houston is currently working to clear cap space for a large offer for Anthony, while the Mavs just traded for Tyson Chandler, one of Anthony's most trusted teammates in New York.
The Knicks still have plenty of confidence that Anthony will return, and they have the ability to offer the most money on a new contract.