Mr David Burnside, the South Antrim Ulster Unionist MP, has urged senior figures in the UUP to personally advise Mr David Trimble that he must resign as party leader.
He issued his call after Mr Trimble's most likely challenger, the East Belfast Ulster Unionist Assembly member Sir Reg Empey, indicated he would not stand against him at the annual conference of the Ulster Unionist Council (UUC) on Saturday week.
Ulster Unionist leaders must be annually ratified at these UUC gatherings.
Mr Burnside and others have been trying to persuade Sir Reg to stand against Mr Trimble but yesterday he said he would only seek the leadership if Mr Trimble stood down.
Asked directly by the Irish News if he would challenge Mr Trimble on March 27th he replied, "No. Basically my position has not changed."
Sir Reg said he was anxious to unite the party rather than split it. He added that as regards the leadership, "my own view is that it is only likely to come about in circumstances where the current leadership decides voluntarily to move on."
His comments would seem to strengthen Mr Trimble's chances of remaining as leader on Saturday week.
Mr Trimble has insisted that he is duty bound for the state of the party and Northern Ireland to seek formal reappointment as leader at the UUC, and if Sir Reg won't stand against him then some other senior challenger must come forward.
So far that has not happened, although Mr Burnside told The Irish Times yesterday that there should be a challenger on Saturday week and he believed Mr Trimble would be challenged.
Mr Burnside repeated that he would not seek the leadership. Indicating that he still saw some hope of Sir Reg becoming leader he said senior party figures should tell Mr Trimble to resign "in the interests of the party and Northern Ireland".