Graveyards and cemeteries were closed to the public in March when lockdown measures were announced.
The regulations were drawn up by the Department of Health but the executive holds the power to change them.
The DUP and UUP back the move, Alliance and Sinn Féin have voiced opposition.
The SDLP is seeking health and scientific advice on the issue.
The public in Derry are also divided over the closure of cemeteries.
Earlier this week a protest was held by people at Derry city cemetery over its continued closure by the council.
However, other members of the public believe the cemeteries should remain shut and that people should stay at home and stay safe until the country is over the worst of the COVID-19 pandemic.
The Catholic Bishop of Derry, the Most Reverend Donal McKeown and the Church of Ireland’s Bishop of Derry and Raphoe, Rev Andrew Forster, have both said the issue around cemeteries and graveyards needed to be looked at again by the Executive.
A British government minister said almost two weeks ago that cemeteries should remain open to the public.
Despite Robert Jenrick’s statement, the Stormont Executive has refused to reopen graveyards and cemeteries.
First Minister Arlene Foster has said she believes it should be possible to reopen cemeteries while Health Minister Robin Swann said he saw no reason not to reopen them, as long as social distancing measures can be implemented.
On Thursday night, Sinn Féin leader Mary Lou McDonald said there was “room for consideration” on the issue, but that the final decision was one for the NI Executive.
Cemeteries in the North of Ireland are operated by councils but the executive holds the legal power over whether to reopen them.
It is understood Chief Medical Officer Dr Michael McBride will take part in today’s executive meeting and provide advice to ministers.
Mrs Foster, speaking to BBC NI’s The View programme on Thursday evening, said a paper from Health Minister Robin Swann was given to executive colleagues last Friday recommending cemeteries reopen.
“Some colleagues decided they felt it wasn’t the right time to go with that advice from the health minister.
“I thought it was at that time, but we have another opportunity tomorrow and I hope that we will come together and that we will give some solace and comfort to those people who want to visit the grave of their loved one.”
She added that it was “the right thing to do”.
Cemeteries remain open in the Republic of Ireland, and Mrs McDonald said: “There is a strong case to be made, I think it will be made tomorrow for looking at those restrictions in terms of the cemeteries and reflecting the kind of measures that we have here in the south.”
The Sinn Fein leader added: “People who now are suffering and who are distraught at the fact that they can’t enter a cemetery – those voices have been heard, I know, by my colleagues and that discussion needs to happen tomorrow around the executive table.”
She cautioned there needed to be a focus on two things – respect for the human needs of families “at the most tragic moment of loss” but also “that we can’t have complacency … that we’re out of danger, because that’s just not true”.