It follows a meeting of the governing body's board and a statement from the SRU is expected on Monday.
A row has been simmering for months over the future direction of the game in Scotland.
Scotland's club sides have been angered by suggestions that some of their policy-making power should be passed to the SRU executive.
Mackay's departure is likely to put added pressure on SRU chief executive Phil Anderton.
Anderton and Mackay were seen as close allies as they attempted to shift the balance of power within the organisation.