Up to 60 employees and union representatives held a protest outside the Guildhall yesterday afternoon over potential job losses.
Around 30 jobs are at risk because of a restructuring plan.
The plan would cut the number of departments from seven to three.
Management and union representatives are due to meet later today.
A spokesperson for Derry City Council said it was committed to progressing with the plan, and a consultation process had begun with employees and their union representatives.
