MIAMI—Carmelo Anthony was slated to sit down with Knicks team president Phil Jackson on Thursday night in what figured to be the final meeting between the star forward and team executives before Anthony decides whether to enter free agency this summer, according to a person familiar with the matter.

Jackson, who was to be joined by new head coach Derek Fisher and general manager Steve Mills, was expected to lay out how both Anthony and the organization could benefit from the 30-year-old opting in for the final year of his contract.

Their main assertion: Were Anthony to begin his free-agency process next summer, as opposed to this summer, he could potentially earn more money because he'd be eligible to earn a higher maximum value—close to $140 million over five years, rather than $129 million—in his next contract. For the team, there would be the added benefit of better calculating how much salary-cap space would be available to accommodate another star player or two.

Time is of the essence. Anthony must notify the Knicks by June 23 whether he will opt out of the final year of his deal, worth $23.5 million, to become a free agent. On the other side of the table, Jackson is expected to leave town Friday to attend his son's wedding in Turkey, as initially reported by the New York Post. (Jackson said during Fisher's introductory press conference Tuesday that he and Mills were planning to meet with Anthony again "soon.")

Thursday's meeting also came amid speculation that the Miami Heat, who are currently playing the San Antonio Spurs in the NBA Finals, might be interested in signing Anthony this summer and creating a "Big Four," with Anthony joining LeBron James, Dwyane Wade and Chris Bosh. But it's too soon to know what will happen with that scenario, given that Miami could very well win a third straight championship with the roster it already has in place. The Heat's stars would all need to reconfigure their current contracts for less money in order to make signing Anthony even a remote possibility.