Farbod Esnaashari of Sports Illustrated reported the news Sunday.
Rumors have swirled around the 2017-18 NBA MVP since mid-November, when ESPN's Adrian Wojnarowski and Tim MacMahon reported both Harden and former teammate Russell Westbrook questioned the "direction of the franchise" after the exits of general manager Daryl Morey and head coach Mike D'Antoni.
Westbrook was later traded to the Washington Wizards for a package that included fellow point guard John Wall, and now, it sounds like the Rockets may be closing in on a second blockbuster deal.
The Nets and Heat are both teams Harden named as preferred destinations along with the Milwaukee Bucks and Philadelphia 76ers, per Shams Charania of The Athletic.
"He has told the Rockets that he wants to be traded to compete for a title elsewhere, and has been resigned to the belief that he can no longer compete for a championship in Houston, sources say," Charania wrote last week.
If a trade is eventually finalized to one of those four teams, it would shift the balance of power in the Eastern Conference.
The Heat are the reigning conference champions after a terrific playoff run that ended with a loss to the Los Angeles Lakers in the Finals, while the Nets are expected to emerge in the contender category with Kevin Durant returning from injury to join Kyrie Irving.
Milwaukee, led by two-time defending MVP Giannis Antetokounmpo, and Philadelphia, with Ben Simmons and Joel Embiid, also have the foundations for high-end success in 2020-21.
The question is whether the team acquiring Harden would be forced to break up their core to make it happen. Speculation has been floated in recent weeks about interest in either Simmons or Irving from Houston, which is trying to leverage its top asset into a massive return package.
It could put Miami, which has plenty of young talent around star forward Jimmy Butler, in the best position to make a deal.
All told, there are still far more questions than answers about the Harden pursuit, but it sounds like the situation could come to a head over the next three days.
The Rockets are scheduled to open the regular season Wednesday against the Oklahoma City Thunder.