Anthony, 34, averaged 16.2 points over 78 games for the Thunder last season.
Free agent forward Luc Richard Mbah a Moute has signed a one-year deal to play with the Los Angeles Clippers.
It's an era of NBA basketball in which contending teams often build a "Big Three" to help them win titles and adding Anthony to the mix in Houston would give the Rockets just that. Mbah A Moute became a key part of the Rockets' franchise best 65-17 record last season.
The Rockets are among the teams that Anthony is reportedly interested in playing for, though money could be an issue.
The Clippers on Monday also officially announced the re-signing of guard Avery Bradley, whose deal was reported last week as a two-year, $25 million pact. "Avery's intensity and proven work ethic will have a direct impact on the performance and personality of this team". The former UCLA standout started a career-high 76 games in his final year in Los Angeles before transitioning back to a role player off the bench during Houston's campaign to the Western Conference Finals.