Executives are reportedly working on a solution that could see the team freed of Anthony's costly expiring contract, looking to offload the deal to a rival that would likely see Anthony waived to enter free agency.
Anthony is soon to be a free agent if the Thunder can't guarantee a trade.
If Anthony does become a free agent, the Rockets won't be the only team interested in his services.
After failing to secure a trade for Anthony last summer, the Rockets will have the opportunity to sign Melo again.
The Heat can surpass the tax to re-sign Wayne Ellington without using any of those vehicles to sign players. It's far from a sure thing, but it looks like the Rockets are making a push to land the veteran sharpshooter.
He failed to earn an All-Star nod for the first time since 2008-09, though his 169 3-pointers made set a new career high.
James's Los Angeles Lakers could also offer Anthony a possible way out of Oklahoma while remaining Banana Boat buddy Wade would also relish the chance to play alongside the former Denver Nugget in South Beach.
But Anthony has averaged 24.1 points and shot 44.9 percent in 15 National Basketball Association seasons and has been one of the NBA's premier scorers of the past 20 years. He is coming off of a career season, where he averaged 13.9 points, 10.8 rebounds and 1.9 blocks.
If he joined the Heat, he could slot in at power forward in a frontcourt with Hassan Whiteside and Josh Richardson.