Kean, who resigned from his position at Ewood Park in September 2012, is in talks with Duli Pengiran Muda Mahkota FC, who compete in Singapore's S.League.
"We are still in talks and will make an announcement at the end of the season [which ends in November], Brunei DPMM club manager Waslimin Momin told the Straits Times.
Rovers global adviser Shebby Singh, who has been heavily critical of Kean in the past, has backed the Scot to succeed in Asia.
"The step up to Premier League manager may have proven difficult, but Steve has all the credentials and it will good for him to get away from all the negativity," Singh told the Singaporean daily newspaper.
"In Brunei, there won't be many influences; he can be his own man and I can safely say that he will excel."
Brunei are currently seventh in the 12-team S.League.