ESPN reported on Wednesday that eight-time All-Star Harden was joining the Nets in a deal also including the Cleveland Cavaliers.
The report said Caris LeVert, Dante Exum, Rodions Kurucs and four first-round picks – and four Nets pick swaps – were heading to Houston.
The Rockets are reportedly sending LeVert to the Indiana Pacers in exchange for Victor Oladipo.
Jarrett Allen and Taurean Prince are said to be joining the Cavs.
The reported move came a day after Harden's frustrations boiled over following a loss to the Los Angeles Lakers.
The Rockets star walked out of his post-game news conference, not before telling the media: "I love this city. I literally have done everything that I can.
"This situation is crazy. It's something that I don't think can be fixed."
Rockets duo John Wall and DeMarcus Cousins were both critical of Harden.
Led by Harden, the Rockets reached the Western Conference Finals in 2015 and 2018, while Houston have three semi-final appearances since he was acquired from the Oklahoma City Thunder in 2012.