A special meeting has been called by the Isles of Scilly Council to examine the conduct of chief executive Philip Hygate, BBC Cornwall understands.
The meeting of the unitary authority's Policy and Resources Committee has been called for Tuesday 30 October.
The meeting is being listed to discuss "employment issues" and will be held in camera.
BBC Cornwall understands it will only debate the work of Mr Hygate, who has been unavailable for comment.
An official notice to be published will simply state the proceedings will be held in secret because of the confidential nature of the issues to be discussed.
Last month, Mr Hygate denied claims he was responsible for an alleged "climate of fear" on the islands.
BBC Cornwall was told by residents they feared losing council contracts or jobs if they disagreed with him.
At the time Mr Hygate said he did not "have the power that some people assert I do have."