Brown traveled to Denver and met with Nuggets CEO Josh Kroenke and general manager Tim Connelly on Sunday night.
Melvin Hunt, who was part of George Karl's coaching staff, was also interviewed for the job, sources said. He's considered a future head coach in the league.
Brown was the fifth candidate to meet with the Nuggets after Hunt, Lionel Hollins, Brian Shaw and Vinny Del Negro.
The Nuggets had shown interest in Doc Rivers before he accepted the Clippers head-coaching job, league sources said.
Brown has been an assistant for the past seven seasons under Spurs coach Gregg Popovich. Before a promotion to the bench, Brown had been the Spurs' player development coach for five years.
With the Spurs' loss of assistant coach Mike Budenholzer to the Atlanta Hawks' head-coaching job, Brown has been expected to be promoted to the top assistant's job under Popovich.
Brown was the Australian national coach and led the Aussies to a strong showing in the 2012 Olympic Games in London. He coached in the Australian National Basketball League for 14 seasons. In nine seasons as a head coach, he won 149 games – the sixth most in league history.
Brown played his college basketball at Boston University under Rick Pitino.
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