According to Adrian Wojnarowski and Marc J. Spears of ESPN.com, the altercation carried over into the locker room.
Green reportedly "challenged" Durant about his upcoming free agency, per Shams Charania of The Athletic, and the argument remained a "simmering issue" Tuesday.
Per Haynes, Green also called Durant "a b---h" several times. The usually quiet Klay Thompson spoke up to his teammates and "stressed the importance of sticking together."
Charania added the Warriors decided Green will sit to "cool off."
Though the 121-116 overtime loss to the Clippers shouldn't worry a team that is 11-3, the infighting could be a greater concern.
Durant is in his third season with Golden State and has helped the squad win the NBA title in each of the last two years, but he is still an outsider compared to the core of Green, Thompson and Stephen Curry. Green has been with the Dubs since 2012, when he was drafted 35th overall in the second round.
The Warriors have enough talent to win another championship even if the players don't have the best chemistry, but they could be in trouble if relationships get too hostile.