"Before I make a decision I am providing an opportunity for the board to comment on the concerns raised and my intention to consider appointing a commissioner to the DHB to replace the current board."
Dr Coleman's letter says he is "committed" to the plan to redevelop Dunedin Hospital.
In a short statement, Mr Butterfield said he had "every confidence" in the board.
"I will be working through the process with the Minister of Health and I will not be commenting further until I have spoken to the Minister," Mr Butterfield said.
Through a spokesman, chief executive Carole Heatly declined to comment.
Board member Richard Thomson declined to comment when contacted.
The proposed action follows months of uncertainty after Dr Coleman confirmed in February he wanted to replace Mr Butterfield with a new chairman, but no appointment was made.
In the meantime, proposed cuts to head off a projected $42 million deficit in 2015-16 met opposition and put pressure on Dr Coleman and local National MPs.
About 1700 people attended meetings in Central Otago last month to protest against possible reductions to Dunstan Hospital services.
Labour health spokeswoman Annette King yesterday urged Dr Coleman to make a decision quickly, because southern health services were suffering from his "indecision".
"I just hope that if he's going to do it, he doesn't dilly-dally round for the next few months.
"This has drifted, and it's drifted at the expense of more money going into the deficit and no resolution of the issues that you face," Mrs King said.
She urged Dr Coleman to examine underlying problems, as there were no quick fixes.
"There is something inherently wrong in the funding. It can't just be the management of the board or otherwise why hasn't the Crown monitor found it?"
Association of Salaried Medical Specialists executive director Ian Powell had mixed feelings about the proposed action, saying it would only work if the right person was appointed.
He expected Dr Coleman would go ahead and install a commissioner, because: "If the board had anything to say to convince the Minister, they would have said it previously".
The senior doctors' union's main concern was the difficult relationship between senior management and the rest of the DHB workforce.
"I think it's a risk [installing a commissioner]. Clearly something had to be done. But we would have preferred that it had been some level of intervention to address the senior management issues.
"That may well be the objective that the Minister has, but it's a very round-about way of doing it."
In a statement yesterday, Dr Coleman said he would make a decision after considering the board's response.
"I am committed to the vital redevelopment of Dunedin Hospital and the provision of high quality health services to all the people of the Southern region.
"The problems at Southern DHB are long standing and have been well documented."
Board's financial woes
2010-11: $200,000 surplus
2011-12: $13.2 million deficit
2012-13: $11.9 million deficit
2013-14: $17.8 million deficit
2014-15: Projected $27 million deficit
2015-16: Could be up to $42 million deficit
Timeline
May, 2010: Otago and Southland district health boards merge to form Southern District Health Board.
August, 2011: National Health Board releases review of Dunedin Hospital calling for widespread culture change as 'demoralised' staff struggle to provide safe services
July 2012: PricewaterhouseCoopers called in for advice after budget blow-out. Later that year it identified $30 million in health cuts. The board paid more than $400,000 for its services.
April 2014: Leaks in Dunedin Hospital's run-down clinical services building prompts urgent repair work costing $1.75 million.
September 2014: The board abandons a plan to upgrade Lakes District Hospital because of its financial position.
October 2014: Draft strategic plan recommends shifting more services to the community.
April 2015: A delay in the Dunedin Hospital clinical services building rebuild is revealed, with a report showing detailed planning work would not be completed until late 2016. Former health minister Tony Ryall had earlier said a completed business case would be considered in 2015.
April 2015: Health Minister Dr Jonathan Coleman denies claims he is considering installing a commissioner after a report is leaked, forecasting a $42 million deficit for 2015-16.
May 2015: Proposed cuts to community-based services including rural hospitals prompts well-attended public meetings and wide public concern.