The current four-week circuit-breaker lockdown ends on Friday.
It saw schools closed for an extended Halloween break and a partial shutdown of the hospitality sector among a myriad of restrictions.
Both Sinn Fein and the DUP said the restrictions would end this week. However, they are locked in disagreement over how to proceed.
The most recent proposal put forward is from Justice Minister Naomi Long. It would fuse Health Minister Robin Swann's one-week extension proposal with Diane Dodds' plans for partially reopening the hospitality sector.
Under the proposal, the circuit break would continue for a further week before the introduction of measures that would allow cafes and coffee shops to reopen and close contact services to resume.
In a bid to break the deadlock, the health minister had tabled a one-week extension to the current restrictions and avoid the cliff edge of all current restrictions falling away. He had wanted another fortnight.
Arlene Foster has apologised for the added uncertainty given she said the restrictions would come to an end.
Michelle O'Neill said on Sunday the hospitality sector could reopen this week with the sale of alcohol prohibited. While pubs and bars would remain closed for at least another fortnight.
However, she has appeared to backtrack on those proposals.
The DUP accused Sinn Fein of a massive u-turn on easing Covid restrictions. Party sources told the Belfast Telegraph Michelle O'Neill has performed a "spectacular backflip" from her previous position on Sunday "under the orders of Dublin SF".
Sinn Fein dismissed the claim as "patent nonsense".
The BBC reported that Ms O'Neill advised First Minister Foster of her intentions ahead of the interview, with the DUP leader advising against issuing such comments.
DUP leader Arlene Foster said the proposal from her economy minister represented a compromise. She said she also wanted support for business increased.
Her party used its veto to block extending the health minister's proposals. Sparking anger from Justice Minister Naomi Long.
She has insisted it is not a case of health versus the economy saying the respective ministers are very aware of each others departments.
The past four-week circuit-breaker lockdown, she said, had cost the economy £400million.
Mrs Foster said economic decisions were taking a huge toll on the public's mental health.
Health Minister Robin Swann tabled a paper on Tuesday advising of an extension of the current restrictions for another two weeks. He later tabled the proposal again opting for just one week.
The DUP has tabled its alternative, which would involve:
The third option, and the one that was most recently considered by the Executive, would see a fusing of Robin Swann's one-week extension proposal and Diane Dodds' plans for partially reopening the hospitality sector.
The circuit break would continue for a further week before the introduction of measures that would allow cafes and coffee shops to reopen and close contact services to resume.
During the meeting on Tuesday, chief medical officer Dr Michael McBride and chief scientific adviser professor Ian Young briefed ministers on the implications of each move on Covid-19 infection rates.
Without an agreement, all current restrictions will automatically expire on Friday.