It comes as 274 new cases of Covid-19 have been detected in the Republic, 166 of them in Dublin.
The Sunday Independent reports that HSE chief Paul Reid told ministers at the Cabinet Covid-19 sub-committee that the testing system will not be able to withstand a second wave of the virus.
He told the Taoiseach, Tánaiste and other senior ministers the HSE currently has no scope to increase capacity beyond carrying out around 14,000 tests per day or 100,000 per week.
Serial testing at meat plants had to be stopped earlier this month due to an increase in demand for swabs in the community.
A spokesperson for the HSE has told the paper that despite a rise in capacity in Ireland, it still maintains relationships overseas to carry out surge testing.
Earlier this week, Mr Reid said the country is at a “very concerning juncture” regarding the performance of the virus.
“We have a couple of choices of which road we might determine that we take,” he warned.
"I don't paint a picture just to be a prophet of doom but it is the facts and it is the data and it is the evidence of where we currently are.
“The bottom line is we stay on the current road as we are and the current trajectory, it will only get worse if we just keep the way we are," Mr Reid added.
Sinn Féin leader Mary Lou McDonald has been critical of the test and trace model, saying it was "disgraceful" that the Government has been unable to reach the 100,000 tests per week capacity.
“For me, the big, big flaw in all of this has been the absolute failure of Government to deliver prompt, testing and tracing,” she said.
“The World Health Organisation (WHO) from day one, page one, told us that the essence of a strong response to this virus is to test, to trace and to isolate.
“Here we are, months after we were promised there would be 100,000 tests a [week], and we are not close to that yet. I think that is disgraceful.”