The Ulster Unionists are expected to announce today which departments Sir Reg Empey and another senior colleague will choose, a spokesman has said.
The party has already opted for the department of health and the department of employment and learning, but there has been no announcement yet about which of these departments the party leader will take.
It had been anticipated that Alan McFarland would be the other ministerial nominee, but a party source has suggested that deputy leader Danny Kennedy could also be named.
Sinn Féin and the SDLP have already made clear which of their nominees will take over at the departments of their choice.
The delay by the Ulster Unionists has prompted rumours of internal dissent within the party and a suggestion that a leadership challenge could emerge as the party's annual general meeting looms later this month. These have been strongly denied.
Under the Ulster Unionist constitution, the party leader has to submit himself for re-election each year. Following the resignation of David Trimble as party leader, Sir Reg defeated Mr McFarland, who is a North Down Assembly member and party chief negotiator.
It is thought that Sir Reg, who was minister at the department of enterprise, trade and investment under the last executive, would opt for the high-profile department of health. However a reliable party source told The Irish Times last night that he could yet be persuaded to opt for the lower profile job to enable him to spend more time on party affairs.