Construction could be allowed to return on a phased basis from April 5th under plans being considered by Government.
The building of public and private homes is expected to be the first to resume.
The Irish Times reports that the plans are being tabled by Ministers after a push by lobbying groups.
The Construction Industry Federation has warned the housing crisis could be extended for at least three years if the sector remains shut.
Meanwhile, the five kilometre travel limit could be expanded to eight or ten kilometres next month, rather than scrapped, if COVID-19 case numbers remain high.
The resumption of some outdoor activities is also being discussed, such as golf or tennis and non-contact sports for children.
An announcement on the easing of certain restrictions will be announced before April 5th, with the next round of changes not expected again until mid-May.
It comes as the Taoiseach refused to speculate on suggestions that tight restrictions could be in place until June.
Speaking yesterday, Micheál Martin said the Government will re-assess the situation at the start of April.
On Newstalk Breakfast with Susan Keogh, a behavioural expert from the ESRI said around 80% of people believe that preventing the spread of the disease is more important than any burden of restrictions.
Dr Shane Timmons, a Research Officer with the Behavioural Research Unit, said there has been a slight increase in socialising among the small cohort of the population who were already gathering together despite the rules.
"There is a balancing act here where there is a slight upward increase in the amount of people going to different locations and their close contacts, but the vast majority are not doing this."
Dr Timmons added that since the outset of the pandemic, his unit has been assessing the 'collective action problem', or the individual sacrifices made by each person for the greater good.
"I think people in Ireland have generally been very good with this, we've seen the majority are willing to comply, are making those sacrifices in not seeing their friends and family and so on," he explained.
"It is the majority of people that are still in on this, but we have seen there has been a decrease in wellbeing over the last few weeks as the restrictions have dragged out.
"We do see that worry is the strongest predictor of complying with restrictions and worry has been quite high.
"We also see that people tend to overestimate how many other people are socialising, so it is important to emphasise that it's a minority of people who are having most of the social activity."
The ESRI also carried out research in the early stage of the pandemic asking people what would have the greatest impact on people coming out of the first lockdown.
The most widely shared things that people wanted to see was permission to meet up with others and the extension of the travel limit.
"Those things are likely to have quite a powerful impact on people and it might help things in their day to day lives," Dr Timmons said.