The nurses' union believes the proposed new structure would strip nursing leaders of their power.
After the New Zealand Nurses' Organisation spoke out in the Otago Daily Times last Saturday, Mr Fleming made contact with organiser Lorraine Lobb.
Mrs Lobb said Mr Fleming had offered to meet her to explain the thinking behind the proposed changes.
The restructuring would appear to remove some power from senior management nurses, whose staff would report to them on professional, rather than operational budget matters.
The proposal is in the formal consultation phase, and the confirmed structure is to be released next month.
The restructure would result in a net loss of 23 management positions.
Mr Fleming wants to dump the chief operating officer and deputy chief executive positions, but the net job cuts will be felt below executive level.
