According to the Cleveland Plain Dealer, the move would free more than $21 million in cap space for the Cavaliers, who are reportedly interested in getting LeBron James, the biggest prize in free agency, to return to Cleveland.
The maximum deal the Cavaliers could give James next season is about $20.7 million. James spent the first seven years of his career in Cleveland before bolting for Miami, where he has won two titles in four years.
Nothing is official until the NBA lifts its moratorium Thursday on signings and trades. But Jack tweeted about the trade "I got news" on Sunday. Jack also listed himself as a Brooklyn Nets point guard on his Twitter profile.
James met in Las Vegas with Miami Heat officials for more than an hour on Wednesday but left the meeting without making a decision on his free agency, ESPN television reported.
James attended the meeting with his agent Rich Paul, while the Heat group included president Pat Riley and general manager Andy Elisburg.
ESPN said that James wanted to talk with his family before deciding whether to stay in Miami or move on. James has talked to several teams.
James might be planning to make up his mind before he leaves on Friday to attend the World Cup final in Brazil.
The US media also reported Wednesday that James' teammate Chris Bosh could sign with the Houston Rockets if James doesn't return. The Rockets have reportedly offered Bosh and four year, $88 million deal.
Jack and 2013 first round draft pick Sergey Karasev would go to the Nets and Tyler Zeller and a 2016 first-round draft pick to the Celtics, who will also acquire Brooklyn's Marcus Thornton.
Cleveland is expected to acquire a future second-round pick from either Boston or Brooklyn to complete the trade.
Jack, a nine-year veteran, averaged 9.5 points and 4.1 assists per game last season in his only year with Cleveland. He owns career averages of 10.9 points and 4.3 assists.
Zeller, in his second year in the league, averaged 5.7 points and 4.0 rebounds with the Cavs last season.