The warning is part of Health Minister Robin Swann’s latest advice to the Executive.
The health paper is also asking the Executive to consider the possible introduction of local, legally enforceable travel restrictions.
Until now, the Executive has only advised against “unnecessary travel”.
It is thought the proposal would be similar to the travel limits introduced in the Republic and by Wales during their first lockdowns.
The paper before the Executive is believed to spell out interventions are needed in late November.
Otherwise, a full lockdown in mid-December would not be enough to prevent hospital services being overwhelmed.
Ministers are discussing the advice from Mr Swann and his officials at Thursday’s Executive meeting this afternoon – the first full meeting since last week’s row over extending some regulations.
On Wednesday, Mr Swann said he would bring a range of options to ministers including restrictions and initiatives, in the hopes of reaching consensus.
He said the measures were aimed at restricting the spread of Covid-19 ahead of Christmas.
NI’s Chief Scientific Adviser Prof Ian Young has said the R-rate – the rate of transmission of the virus – in the North of Ireland is currently sitting at “around one”, and has risen since school reopened two weeks ago.
The chief executive of Hospitality Ulster Colin Neill said not being able to open on 27 November would be “devastating” for businesses.
“If we are not open, the current funding does not save the businesses, and furlough is not free,” he said.
“We have to have a business there paying £30 per person, per week to keep people on furlough.”
Dr Tom Black, chair of the British Medical Association (BMA) in NI, said easing restrictions now would see “us paying the price further down the road”.
“The big problem is that we are still running at very high levels in the over 60s, our hospital beds are blocked, our ICUs are blocked,” he said.