Irving was handed an indefinite team-imposed suspension by the Nets, for at least five games, after the seven-time All-Star shared an allegedly antisemitic film and book on social media a fortnight ago.
The Nets point guard's minimum five-game ban elapsed after Brooklyn won 110-95 over the Los Angeles Clippers on Saturday.
Brooklyn owner Joe Tsai put out a statement on Friday stating that "the Nets and Kyrie, together with the NBA and NBPA, are working constructively toward a process of forgiveness, healing and education". Irving met with Tsai this week along with NBA commissioner Adam Silver as they move toward a resolution on the saga.
Nets head coach Jacque Vaughn confirmed that Irving would not play in Sunday's game with the Los Angeles Lakers and added there was no timetable for his return.
"The good thing is Joe put out that statement that shows where the collaboration or alignment is right now," Vaughn told reporters. "I have no idea or timetable at all.
"I do know not available [for Sunday], I have been told that. So I can give you that."
Durant, who top scored with 27 points against the Clippers, said he was eager for Irving to return to the court and move on from the episode.
"His spirit is high," Durant told reporters about Irving. "[He's] looking forward to playing again. He's a gamer. He loves to play. Hopefully all this stuff is over with, we can move past it and get him back on the floor soon.
"That's been out of our control. And as players we try to lock in on the game, practices. We just try to lock in and whenever that figures itself out, it will. That's over a lot of our heads right now so we just got to control what we can."
The Nets showed they can win without Irving, claiming victories in four of the five games he has missed during this ban, with Seth Curry popping up with 22 points off the bench against the Clippers following off-season ankle surgery.
Durant added: "We're going to have to be one of those teams that any given night, somebody will have to step up and make huge plays for us.
"Obviously we're missing [Irving], so we're going to have to look for where those points are going to come from. I think the guys are doing it as a group."