Nash also confirmed that Irving practiced Tuesday for the first time in over two weeks.
Kyrie had been away from the team for what the Nets called personal reasons, and he has now missed Brooklyn's past seven games.
Per Chris Sheridan of BasketballNews.com, Irving was asked for the reason behind his absence Tuesday and said: "A lot of family and personal stuff going on. I just want to leave it at that."
Andrews reported that the NBA fined Irving $50,000 for violating the league's health and safety protocols related to COVID-19 after videos surfaced on social media showing him maskless at an apparent family birthday party during his absence.
ESPN's Bobby Marks added that Irving had to forfeit his salary for the two games he missed during a five-game quarantine period, costing him a total of $816,898.
Now that Kyrie is set to return, the Nets could have all three members of their superstar triumvirate in the lineup together for the first time Wednesday against the Cavs.
Irving has not played since the Nets acquired James Harden from the Houston Rockets in a four-team deal that also included the Indiana Pacers and Cavaliers. Brooklyn parted ways with several depth players to land Harden, including Caris LeVert, Jarrett Allen, Taurean Prince and Rodions Kurucs.
Harden has looked excellent in his two games as a member of the Nets, averaging 33.0 points, 13.0 assists and 9.0 rebounds.
Irving signed with the Nets prior to the 2019-20 season along with Kevin Durant. KD missed the entire 2019-20 campaign while recovering from a torn Achilles, while Kyrie missed all but 20 games due to multiple injuries.
Kyrie was effective when he played, and that has been the case once again this season, as he is averaging 27.1 points, 6.1 assists and 5.3 rebounds per game.
The Nets are fifth in the Eastern Conference at 9-6, but they have won four in a row and are 2-0 since Harden's arrival. With Irving joining Harden and Durant, they figure to be even more dangerous.
Against a struggling Cavs team that has lost three of its past four games and five of its past seven, the Nets could be poised to put up big numbers in a lopsided win that cements them as one of the teams to beat in the Eastern Conference.