Per The Athletic's Alex Schiffer, Nets general manager Sean Marks announced the news during a conference call Wednesday.
There have been 15 confirmed coronavirus cases involving NBA players, owners or team personnel. Marcus Smart, Rudy Gobert, Donovan Mitchell and Christian Wood have since been cleared following their diagnoses.
Two unnamed players for the Los Angeles Lakers were declared symptom-free Tuesday, a team spokeswoman told Mike Bresnahan of Spectrum SportsNet.
On March 17, the Nets announced four players tested positive for COVID-19, and one of them was experiencing symptoms.
The team also stated all four players were "isolated and under the care of team physicians."
Durant told Shams Charania of The Athletic and Stadium that he was one of the players who had the virus: "Everyone be careful, take care of yourself and quarantine. We're going to get through this."
The Nets' last game was on March 10 before the NBA suspended its season the next evening because of the coronavirus pandemic.
Durant moved to Brooklyn in a sign-and-trade last July but hasn't appeared in a game while rehabbing the ruptured Achilles he suffered in the 2019 NBA Finals with the Golden State Warriors.