Anthony has until Monday to officially inform the team of his plans.
Knicks president Phil Jackson said recently that he hoped Anthony would consider opting into the final year of his contract and testing free agency in the summer of 2015. Jackson has privately expressed that hope to Anthony several times since the end of the regular season.
The Chicago Bulls are one of several teams with whom Anthony would consider signing, according to sources.
According to league sources, Anthony has talked to at least one high-profile person who lives in Chicago about what it's like to be famous in the Windy City.
The Bulls also have reportedly done their due diligence on Anthony in recent days. According to a report in the Chicago Sun-Times, Bulls coach Tom Thibodeau has reached out to some of Anthony's former coaches to inquire about the seven-time All-Star.
Anthony can sign a maximum contract worth $129 million over five years with the Knicks. He can ink a maximum deal worth $96 million over four years with another team.
Anthony has discussed the possibility of accepting less than a maximum contract to help the team that he signs with attract additional free agents.