Simon Harris says the country appears to be on track for a further easing of restrictions in May, but the measures are likely to happen on a phased basis rather than all at once.
Hairdressers, barbers retail and the remainder of construction are all expected to reopen in May.
However, the Higher Education Minister said he hopes the Government will also be able to give a detailed plan for June and July next week.
Health experts have continued to emphasise the need for a cautious reopening, but Government has been increasingly upbeat about the prospects of a wider reopening next month.
It comes amid falling COVID-19 case numbers, a major reduction in hospital numbers, and the ongoing scaling-up of the vaccination programme.
On Lunchtime Live, Simon Harris said people will find out very soon what the next steps will be in easing restrictions.
He said: “I would say we have indicated in the month of May we will be looking at retail, personal services and the rest of construction.
"Next week - probably on Tuesday… the Government will meet and put the plan in place for May - and I hope for June and July. We’ll be able to indicate to people when things will be reopening.
“There’s a very decent chance of a phased reopening in the month of May.
"We [do] need to see how this week goes. It will probably be on a phased basis - you’re unlikely to see everything on one day in May."
'Hopeful and optimistic'
Minister Harris said Ireland is in better shape in tackling the virus than we have been "in a hell of a long time" - saying he himself is "more hopeful and optimistic" than he has been in months.
He said he's also hopeful more college and university students will be able to return to campus by September, with a mix of rapid testing and vaccination used to facilitate a return to in-person classes.
There was controversy over the weekend after the prospect of vaccinating under-30s before older age groups was floated by Health Minister Stephen Donnelly.
However, he then quickly ruled out the idea - saying there's no plan or proposal to do so.
Earlier, Minister Harris said Government stands behind his Cabinet colleague after the latest communications blunder.
On Lunchtime Live, Minister Harris - himself a former Health Minister - said the "chopping and changing" of the vaccine plans so far has been a result of public health advice and vaccine supply issues.
He suggested it's now vital to "get on and deliver it... [and] get jabs in arms as quickly as possible".