Health Minister Robin Swann is updating the executive about the mounting pressure on Northern Ireland hospitals.
It follows what health officials described as the worst 48 hours for health trusts since the pandemic began.
The six trusts have warned that by the third week of January hospitals could be dealing with double the number of Covid-19 patients.
First Minister Arlene Foster has said there are few options left to curb the crisis, apart from a possible curfew.
Speaking on Monday, Mrs Foster and Deputy First Minister Michelle O’Neill said while Northern Ireland was past the peak of new cases, the lag between people becoming infected and needing hospital treatment meant inpatient numbers were yet to hit their peak.
Mrs Foster said the latest modelling showed Northern Ireland’s so-called R-number – a measure of the coronavirus infection rate – was sitting at about 1.1 or 1.2.
That is a drop from an estimated 1.8 earlier this month.
Things were “moving in the right direction” with a reduction in the number of new cases, said Mrs Foster, but she warned that people needed to “ready themselves” for strain on the health service in the next few weeks.
Northern Ireland’s chief medical officer Dr Michael McBride said it was estimated that on average about one in 60 people have Covid-19 in Northern Ireland.
He said the rising number of cases was a “payback” for the relaxation of restrictions in December.
New lockdown restrictions came into force in Northern Ireland on Friday 8 January, meaning people can only leave their home for essential reasons.
The chief scientific adviser Prof Ian Young said while compliance with the stay-at-home order was better than it was at the start of December, it was still not as good as it was in the first lockdown in March.
At Tuesday’s executive meeting, ministers are also expected to agree a crackdown on large retailers that are keeping open the non-essential side of their businesses.
Amid the pressure on the health service, health trusts have said more cancer operations could be cancelled.
The Belfast Health Trust has already cancelled urgent cancer surgeries.
Father James O’Reilly, a chaplain at Antrim Area Hospital, said he has been called to the hospital almost every day in the past year to give Covid-19 patients their last rites and to provide comfort to families and staff.
Speaking to BBC Radio Ulster’s Good Morning Ulster programme he said: “You can see the toll it’s taking on the nurses and doctors now.
“They are giving everything and quite honestly they don’t have much more to give it seems.
“That’s a scary thought because they’re our last line of defence against this disease.”
As of Monday evening, almost 92,000 people in Northern Ireland had received at least one dose of a Covid-19 vaccine.
Dr Frances O’Hagan, whose clinic in Armagh city began vaccinating people aged over 80 last week, expects to have administered the jab to more than 300 patients by the end of the week.
She said she hoped to get more stock of the vaccines “very shortly” for the next groups on the priority list.
“We are ready to go… we will get those [vaccines] into patients’ arms as soon as they are given us,” she added.