Junior Health Minister Alex White said that he hopes to have a minimum price for alcohol in place by the middle of next year.
Alex White opened a conference on alcohol and its affect on mental health in Dublin where groups came together to discuss harmful drinking.
Last month the Government laid out the national substance misuse strategy - the central plank of which is the introduction of minimum prices per unit of alcohol.
Minister Alex White says that part of the delay is to do with agreeing a price with the authorities in the North.
Campaigners have expressed frustration at the pace of change, something Minister White agrees with.
"I could understand - and actually...sometimes shares people's frustration - at how long it sometimes takes us in Government to bring forward proposals and put them into actual law," he said.
"We've made massive strides on this now, in terms of getting the Government to authorise the drafting of the legislation - so my earnest hope would be that sometime in early to mid-next year that we could have this in place."