No deal was imminent Wednesday, but the Knicks and Rockets are confident that they have a willing third-team trade partner, the sources said.
The fourth team was needed to move a particular player contract that neither the Knicks nor Rockets could or would accept in the deal, league sources said.
Anthony, 33, has two years and $54 million left on his contract.
The complexity of including multiple teams and assets in a deal creates time-consuming challenges, and there's no guarantee that a deal can be reached.
Nevertheless, New York has been pushing hard to unload Anthony in recent weeks, although it hasn't necessarily changed an asking price that makes the deal a challenge for Houston, league sources said. The Knicks aren't interested in the Rockets' older players and big contracts, so new teams have to be brought into the deal to find a way to satisfy the Knicks.
Anthony is willing to waive his no-trade clause for a deal to the Rockets or Cleveland Cavaliers, league sources said. The Cavaliers haven't abandoned pursuit of Anthony, league sources said.
Through 14 NBA seasons, Anthony, a 10-time All-Star, has averaged nearly 25 points a game. He has played the past seven seasons with the Knicks, who say they're committed to rebuilding around Kristaps Porzingis and younger players.
The Knicks' front office has been privately saying that the organization's marching orders are now focusing on players 25 years old and younger, league sources said.