The team and Brown have a handshake agreement, and an official announcement is expected on Wednesday, the Akron-Beacon Journal reported.
Brown, 43, came to Cleveland in 2005 - his first head coaching job - and guided the Cavaliers to the 2007 NBA Finals.
He was named NBA Coach of the Year for leading the team to a league-best 66 wins in 2009. His team lost to the Orlando Magic in the 2009 conference finals and the Boston Celtics in the 2010 conference semi-finals, leading to his dismissal.
He also succeeded Phil Jackson as the head coach of the Lakers in 2011 but was fired early the next season.
Charlotte Bobcats coach Mike Dunlap is out after one season with the team.
Dunlap finished his lone season in Charlotte at 21-61, the second-worst record in the Eastern Conference, one game ahead of the Orlando Magic.
Indiana Pacers forward Paul George has been named the NBA's Most Improved Player, receiving 52 first-place votes from a panel of 120 media members.
The third-year veteran received 311 of a possible 1,080 points. Greivis Vasquez of New Orleans (146 points, 13 first-place votes) and the Milwaukee Bucks' Larry Sanders (141 points, 10 first-place votes) finished second and third, respectively.
George had 23 double-doubles during the regular season and averaged a team-high 17.4 points along with 7.6 rebounds, 4.7 assists and 1.8 steals.