An executive meeting in London next weekend will hear claims that Sean Rogers, who is due to take over as chair next May, and Sandi Marshall have brought the 40-year-old association into disrepute.
Grievance procedures have been taken out against them by press officer Margaret Morrissey and office administrator Judy Marland. They are refusing to work with Mr Rogers and Ms Marshall.
The first items on the agenda for the meeting of the charity's trustees will be the removal of the two.
Ian Price, chairman, said: "I have on the best evidence presented to me prepared an agenda to seek the views of the trustees. At the end of the day the decision will be theirs. It is down to the trustees to sort out."
The meeting brings to a head disputes over who runs the organisation - staff or trustees - which have escalated in the past few months after the resignation of Michael Pepper as chief executive.
In September, the two camps agreed a stafftrustee management committee would review working practices and draw up a job specification for the chief executive. The committee has yet to meet because staff have suspended co-operation.
Bob Elliott, of the MSF union, said: "We have every confidence in the chairman's ability to take this very difficult problem to the meeting and ensure that the staff's concerns are properly considered.
"While we can understand the public's interest in what is going on, we would prefer to be left to deal with our own problems without the media spotlight on us."
Sandi Marshall said: "Clearly, as a trustee with responsibility to the organisation as a whole, I feel unable to comment at this stage. I will continue to work in the best interests of the charity."
Sean Rogers was not available for comment.