The National Public Health Emergency Team (Nphet) will assess whether Level 3 is working or not on Thursday.
There has been just under 8,000 cases in the last two weeks, and the 14-day incidence rate is now 167 per 100,000 people, a rise of over 40 per cent in the past week.
Dublin, which has been under Level 3 restrictions longer than any other county, had shown some signs of stabilising, but cases have started to grow again.
Chief Medical Officer Dr Tony Holohan says Nphet would like to see some encouraging signs before they meet on Thursday.
"We will be looking at how well we believe the current measures are working. We would like to see some encouraging signs by Thursday of this week."
Nphet is also considering whether masks should be used in outdoor settings.
But Dr Ronan Glynn says a decision is not imminent.
"I think before we think about extending mask use more generally, it's really important at this point that people focus on using them appropriately," Dr Glynn said.
"I will again highlight the importance of people wearing masks where they can wear masks, as opposed to visors. Visors are an acceptable alternative for a very small proportion of our population who can't wear masks for a variety of reasons."
This comes as an emergency meeting will take place in Stormont later today on introducing Covid-19 restrictions in Northern Ireland.
A four to six week lockdown has been recommended by health officials in the North after 877 cases of the disease were detected yesterday.
If the measures are introduced, it may have a knock-on effect for border counties.
