Announcements expected next week "will be welcomed" by the hospitality industry, the deputy first minister has said.
Michelle O'Neill told the BBC's Sunday Politics programme that Monday and Thursday would be "significant days".
"We want to keep giving people that wee bit more to try to get back to some semblance of normality," she said.
Ms O'Neill said she did not feel "any pressure whatsoever" from the Republic of Ireland's reopening.
It began a second phase of easing out of lockdown last weekend, and all travel restrictions are to be lifted by 29 June.
It has been reported that hairdressers will reopen there before the end of the month.
"There's other sectors out there that are now asking for an indicative date and I think it's important that we give them all indicative dates," said the Sinn Féin deputy leader.
'We don't want a second wave'
Ms O'Neill said the focus was also on trying to "avoid a second wave if we can".
"I want the hospitality to open up, but imagine if we were to open up now and have to shut everything down in four or six weeks?" she said.
"We're working our way through our plan gradually and incrementally. We're certainly in a good place, making positive steps forward, but we need to do it gradually."
The prospect of a change to the 2m (6ft) rule was also raised on the programme.
It has been the subject of growing debate in the UK over recent days, with Chancellor Rishi Sunak confirming on Sunday the government had commissioned a review into the rule.
Ms O'Neill said she is "open minded" on a possible reduction, but that any decision must be "guided by the scientific evidence and the medical evidence".
"In all of this, it's about balance, primacy has to be given to public health," she said.
She said she would "continue to keep all of these things under review".
'We can't have half a High Street'
Aodhán Connolly, director of the Northern Ireland Retail Consortium, cautioned the staggered reopening of businesses would create issues.
"The other side is that half a High Street open isn't really good enough to keep things sustained," he said.
"Because there is this symbiotic relationship, especially in Northern Ireland, between hospitality and leisure and retail.
"We are trying to get people to go into towns and spend their time as well as their money."
He added businesses were making efforts to adapt and would need to reach a "critical mass" of customers to be sustainable.