The meetings have not been set up because the teams are not yet allowed to contact free agents. But Anthony has decided he will give those three teams a chance to recruit him when they are able to. Anthony's camp informed the Knicks of his decision to visit the three teams.
While there has been speculation that Chicago is at the top of Anthony's list of potential destinations, one source said there is no true favorite in his mind.
The New York Knicks, who can offer Anthony $33 million more than any other team, are also still very much alive in bringing back the All-Star forward.
Though the Los Angeles Lakers are not on Anthony's current list, Kobe Bryant plans to recruit him to the team. Bryant, who is close with Anthony, spoke to him by telephone when they were in separate parts of Europe earlier this week.
Bryant told ESPN.com in a text message that he plans to meet with Anthony, as well.
While there are still chances for other opportunities to develop, the Rockets, Mavericks and Bulls appear to be the Knicks' biggest challengers thus far.
"Those three teams plus the Knicks seem to be the ones he's going to consider," one source said.