Deputy chairman Simon Eddy said the organisation was in the process of a review and had been working closely with Brown to improve its financial performance.
As part of that review, Brown offered his resignation and will finish up on June 27.
''Anything about Markham being pushed would be highly speculative,'' Eddy said.
''The situation is as the press release states. BBO is in the process of a wholesale review of its structure ... and the reason for that is because of the financial situation that the organisation is in which is obviously fairly public knowledge.
''We've declared a number of losses over a number of years and part of the process of looking at how to improve the financial position of the organisation includes looking at how we run the organisation from top to bottom.
''As part of that we've had discussions with Markham and the rest of the organisation's staff, and Markham offered his resignation in order to assist BBO in strengthening its financial position.''
Eddy said BBO's accounts for the previous financial period were awaiting auditing and would be made public within the next two months.
BBO reported a loss of $13,166 for the financial period ending December 31, 2012.
That loss followed a deficit of $36,787 recorded during the previous period and meant BBO started 2013 with negative equity of $52,832.
Asked if there would be any job losses, Eddy said he could not comment on staffing matters.
However, he said the board was not going to rush into finding a replacement for Brown.
''We have not come to any conclusions on a replacement yet. Markham's resignation comes as part of an overall review and we are not through that process.
''We won't be pre-empting the outcome of how that structure looks. There could be more adjustment to be made within the organisation, but in the interim the organisation will be run more directly by the board.''
Brown, who assumed the role of general manager in November 2010, could not be reached for comment but issued a statement.
''Whilst I have enjoyed the challenges and rewards of my role at Basketball Otago, I have been thinking for some time about the next steps for me career-wise,'' Brown wrote.
''The timing of the review and my choice in direction for my career has also worked in well with my wife's selection to the Silver Ferns for the Commonwealth Games.
''She [Jodi Brown] missed her last opportunity at the Commonwealth Games in 2006 due to her knee injury at the 11th hour which was just gutting for her.
"She is really excited about this opportunity but, with our family being young, an important thing I can do for her is make sure the girls are well looked after at home during the demanding build-up.
''I would love to be involved in the sports industry going forward, and in the immediate future will be working to help the OceanaGold Nuggets and Gold Rush finish their seasons as the Nuggets push for a playoff spot and the Gold Rush, who have qualified for the finals, try and take the title again.''
