O’Neill mentioned she was assured the powersharing govt may agree a timetable for the reopening of extra sections of society at a gathering on Thursday.
First Minister Arlene Foster has already expressed hope that opening dates for close-contact companies, corresponding to hairdressers and beauticians, and non-essential retail might be introduced later this week.
The hospitality sector can be hopeful that it’d get some excellent news on Thursday, notably in respect of out of doors buying and selling.
Northern Eire took some additional gradual steps out of lockdown on Monday.
The rest of post-primary college students, years eight to 11, returned to colleges whereas a restricted variety of outdoor-focused stores, corresponding to backyard centres and automotive dealerships, reopened.
The “keep at dwelling” messaging has additionally been changed with a “keep native” recommendation.
On the weekend, Northern Eire reached the milestone of 1 million vaccine jabs having been given.
On the prospect of additional bulletins on Thursday, Ms O’Neill advised BBC Radio Ulster: “I wouldn’t wish to pre-empt the Government selections on Thursday, however I believe it’s truthful to say that we’re more and more assured in our capability to have the ability to make extra progress.
“We’ve, over the weekend clearly, reached the a million vaccine mark, which was clearly very encouraging and offers us nice hope that we’re making our manner out of this pandemic.
“So I’m hopeful that by Thursday we’ll have the ability to announce dates for different issues having the ability to open up as a result of, for a mixture of causes, the elements look good the place we’ve got the headroom on which to have the ability to transfer.”