LeBron James has his new coach.
The Indianapolis Star also reported that Brown is Cleveland's choice.
Brown, 35, has spent the last two years as Pacers head coach Rick Carlisle's top assistant.
The Cavs also contacted John Calipari, but the Memphis Tigers coach has said he is "not a candidate" in the Cavaliers' search for a head coach.
Cleveland, which is also looking to bolster its front-office ranks, also reached out to Detroit Pistons coach Larry Brown, who has denied meeting with Cavs officials about seeking the team's presidency.
The hiring of Mike Brown could enhance the likelihood that Larry Brown would accept the post as the Cavs' president. Mike Brown was an assistant for three seasons under Spurs coach Gregg Popovich, who is a friend of Larry Brown's, the New York Times reported Monday.
The Willoughby News-Herald (Ohio) reported Sunday that Larry Brown had until Monday to inform the Cavaliers if he would take the post.
Cleveland finished 42-40 in the 2004-05 season, but lost the tiebreaker to the New Jersey Nets and missed the playoffs.