"In addition, we have an outline for an agreement in place and hope to sign a contract within the next few days."
Jackson, the most successful coach of all time in the NBA, ended his stellar career after the Lakers were swept by the Dallas Mavericks in the second round of the playoffs earlier this month.
The 65-year-old had led the Chicago Bulls to six NBA championships in the 1990s, and the Lakers to five since.
Following Jackson's departure, the Lakers narrowed their search for a replacement down to Brown, former Houston Rockets coach Rick Adelman and Lakers assistant Brian Shaw according to U.S. media reports.
Brown had a 272-138 record with the Cavaliers but the team failed to make the Eastern Conference finals last year after it posted the NBA's best regular-season record.
He compiled a 42-29 post-season record in Cleveland and brought the team to at least the second round of the playoffs in each of his five seasons. The Cavaliers lost to the San Antonio Spurs in the 2007 NBA finals.
(Writing by Mark Lamport-Stokes; Editing by Ken Ferris)
