The 50-year-old guided the Cleveland Cavaliers to an NBA Finals appearance in 2007 and has spent the past four seasons on Steve Kerr's coaching staff.
Brown registered a 305-187 mark across two stints as Cleveland's bench boss, including a pair of 60-win seasons. The former NBA Coach of the Year was linked to the New York Knicks' job opening earlier in the summer.
Indiana fired head coach Nate McMillan following a first-round sweep to the Miami Heat. It was the club's fourth straight opening-round postseason exit under McMillan.
Mike D'Antoni, Becky Hammon, Chauncey Billups, and Dave Joerger are reportedly among the other rumored candidates for the Pacers gig.