Deputy First Minister Michelle O'Neill believes there is a "danger" in analysing Northern Ireland's R rate every day as the figure needs time to stabilise.
The R rate - Covid-19's infection gauge - currently stands at 0.9 here.
It must remain below one to avoid exponential growth in cases.
The easing of the lockdown regulations is dependent on the R rate and Ms O'Neill said she was "a bit disappointed" after learning the R value stood at 0.9 on Friday.
Speaking during yesterday's Covid-19 daily briefing alongside First Minister Arlene Foster, Sinn Fein's northern leader hopes an update on the R rate can be provided on Thursday.
"I was a bit disappointed where our R rate was sitting and I know it takes a bit of time," Ms O'Neill said.
"There's a danger in analysing it every day because you have to give it time to stabilise and be steady for a number of days.
"We hope to be in the position to have an analysis of all of that for Thursday's Executive meeting and we will be able to say more about it then.
"Certainly, I think a lot of people were surprised that we were sitting at 0.8/0.9 at the end of last week, but we will be able to say more about that later in the week."
Despite a drop in the number of positive coronavirus tests, hospital admissions and Covid-19 related deaths, Mrs Foster said the R rate is based on where the virus is in the community.
She stressed, however, that the more relaxations that are put forward, the more the virus can spread.
"We have to assess those relaxations [that were announced] on May 15, which came into place on May 18, and what impact that they have had on the transmission of the virus - because if you're infected with Covid-19, you won't be going into hospital until about 10 days after that," Mrs Foster added.
"The number of general hospital admissions, certainly last Thursday, had increased slightly.
"We have to take all of that into consideration when we look at the overall picture and we need to be able to move forward on a step by step basis."
Mrs Foster also said that the Executive wants Northern Ireland to return to normality as quickly as possible.
"We do, of course, want to make sure that people aren't inconvenienced and that these restrictions aren't in place any longer than they need to be," she stated.
"We have to take into consideration where the virus is at after relaxations.
"We need to pause for a while, see where it's at after that relaxation and then if things are still below one then we can make the next step forward.
"That's why it is a phased return and that's why we're moving in the fashion that we are."
The First Minister also said if the rate of transmission continues to fall, they will consider easing further restrictions.
The R rate in the Republic of Ireland is around 0.5-0.7.