Anthony didn't fit in alongside Russell Westbrook and Paul George after being acquired from the New York Knicks before the start of last season.
The 34-year-old New York City native averaged a career-low 16.2 points along with 5.8 rebounds and 1.3 assists across 78 games for the Thunder. He also shot a career-worst 40.4 percent from the field.
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It raised questions about how to make him more effective during the final year of his contract in 2018-19. One of the ideas was moving him to the bench to give him more on-ball opportunities as part of the second unit when Westbrook or George was off the court.
Anthony quickly shot down that potential plan.
"Yeah, I'm not sacrificing no bench role," Anthony told reporters in April. "That's out of the question."
Last week, Adrian Wojnarowski and Royce Young of ESPN.com reported a breakup between Anthony and the Thunder was "inevitable," with the team potentially earning "over $100 million in cost savings."
Whether joining the Rockets would lead to improved results isn't clear. He'd likely still be the third option behind James Harden and Chris Paul. But it's probably worth a shot for Houston as it looks to overcome the Golden State Warriors and the now LeBron James-led Los Angeles Lakers in the West.