Restaurants that do not serve alcohol may also be permitted to reopen outdoors from the same date as part of relaxations to Coronavirus restrictions for the hospitality industry.
In tourism, it is proposed some areas such as self-contained accommodation and static caravan sites could reopen in early May.
They are among the proposals submitted to the Stormont Executive’s coronavirus taskforce by Economy Minister Diane Dodds.
The reopening of outdoor visitor attractions is also understood to be up for discussion.
The North of Ireland went back into lockdown on Boxing Day, December 26.
The Executive will have its next formal review of Covid-19 restrictions when it meets next Thursday, April 15.
A number of lockdown restrictions will be eased from April 12, including the reopening of garden centres and car washes.
Contactless click-and-collect for all non-essential retail will also resume on Monday.
First Minister Arlene Foster has said she hopes the Executive will be able to give a timeline for the reopening of hairdressers, beauticians and non-essential retail following their meeting next week.
She said: “I don’t have the paper in front of me but I do know that Diane has submitted tourism and hospitality measures as well as the reopening of retail and close-contact services.”
April 19 is said to be to early to give notice to businesses to reopen and an extra week would allow them to prepare fully for opening up their businesses again to the public.
Mrs Foster refused to be drawn on whether April 26 is a date being proposed by the Economy Minister, but said ministers wanted to give people certainty and time to prepare.
“Obviously there are many people who have been waiting for this,” the DUP leader said.
“We know that close-contact services opened in Scotland this week, already opened in Wales, therefore people are waiting eagerly to see when the Executive makes those decisions.”
Mrs Foster said she hoped ministers would be able to reach a consensus on reopening some sectors as the number of daily Covid-19 cases continues to fall.
She said: “I do hope colleagues will recognise given the fact that the Covid numbers continue to fall and we are very thankful for that, given that vaccination continues to go very well in Northern Ireland, and given the economic impact that these restrictions are having, I hope that we are able to come to a decision which gives dates to people when we next review these matters.”
Tags: