Northern Ireland's stay-at-home order was lifted on Tuesday to allow non-essential shops to resume business through click and collect services.
Mrs Foster said Tuesday marked a "milestone day that signals our confidence in the way ahead" in the battle against Covid-19.
In a video posted to Twitter on Wednesday, Ms O'Neill said the executive is "hoping" to have more information on dates by Thursday and said earlier that she expected ministers would agree a timetable of reopenings that will cover several months.
Health minister Robin Swann Swann said yesterday the “scales are tipping” in favour of accelerating the pace of lockdown exit.
Mrs Foster had already expressed hope opening dates for close-contact services, such as hairdressers and beauticians, and non-essential retail will be announced after Thursday’s meeting.
The hospitality sector is also hopeful that it might get some good news, particularly in respect of outdoor trading.
What rules were relaxed on Tuesday?
Here is a full list of the changes announced earlier this week:
Up to 10 people (including children) from two households can meet outdoors in a private garden
Up to 15 people (including coaches) can take part in structured outdoor sports training, through clubs or individuals affiliated to recognised sports governing bodies or representative organisations for sport and physical activity
The number permitted to attend marriages, civil partnerships and funerals, will be informed by a risk assessment for the venue
Contactless ‘click and collect’ is permitted for all retail
Outdoor retail (as defined in the regulations) is permitted to reopen
Potential marriage and civil partnership customers may view the facilities of venues used for marriages and civil partnerships, such as hotels and other venues, restricted to a maximum of four customers per visit
The ‘stay at home’ provision has been removed from legislation. A ‘stay local’ and ‘work from home’ message is in place
In Northern Ireland on Wednesday, there was one further death of a patient who had previously tested positive for Covid-19.
Another 97 cases of the virus were recorded by the department of health.
As of Wednesday morning, there were 70 Covid-positive patients in hospital, of whom eight were in intensive care.
Meanwhile, an estimated 54.5 per cent of people were likely to have Covid-19 antibodies in the week to March 28 - up from 50.0 per cent in the previous week, according to Office for National Statistic figures.
An estimated 54.9 per cent of people in private households in England were likely to have tested positive for Covid-19 antibodies in the week to March 28, according to the - largely unchanged on the previous two weeks.
The presence of Covid-19 antibodies suggests someone has had the infection in the past or has been vaccinated.
The ONS said antibody positivity has levelled off in England, Wales and Scotland. In Wales, the latest estimate is 49.1 per cent and for Scotland, it is 46 per cent.