The DUP has said it believes six departments may be sufficient to run the Stormont Executive.
There are 11 devolved departments and 14 ministers. The DUP has tabled a motion for debate at the Assembly on Monday calling for a reduction.
One of the motion's sponsors, Strangford MLA Simon Hamilton, said six may be a reasonable target to aim for.
"We used to have six and I think that should at least be a target number to get it down to," he said.
"I don't want to put specifics on it, but much less than we have is acceptable.
"When you look at the Scottish example, they are functioning with six down from something like nine. I think that is a sensible target to be going for."
However, Ulster Unionist leader Sir Reg Empey said it was "a mere mirage" that reducing the number of departments would save money.
"All that a reduction in departments will mean is a re-badging exercise as the total number of civil servants will remain the same," he said.
"In any event, if a department is too big with diverse functions, it can be less efficient than two departments with clearly defined core functions."
He said "the irony" was that a day later, the DUP would be "asking for an increase in the number of departments with the devolution of policing and justice".