The Detroit Free Press reported Friday that Frank will receive a three-year contract with a club option for a fourth year.
Frank is expected to be introduced by the team next week, the paper said. He spent last season as the lead assistant coach for the Boston Celtics.
The native of northern New Jersey began his coaching career on January 26, 2004 when he succeeded Byron Scott as head coach of the Nets. He immediately guided them to 13 straight victories, setting a new NBA record for the most consecutive wins by a head coach to begin a career.
The Nets enjoyed moderate success under Frank over the next several seasons, making the playoffs four straight times and winning the Atlantic Division twice.
However, after two straight years of failing to make the playoffs, the Nets began the 2009-10 season with 18 straight losses -- 16 of those under Frank -- who was fired on November 29, 2009.
The 40-year-old finished his tenure in New Jersey with a 225-241 record.
Frank would replace John Kuester, who was fired after going 57-107 over two contentious seasons, including a 30-52 mark last season.