Prof McConkey, head of the Department of International Health and Tropical Medicine at the Royal College of Surgeons in Ireland (RCSI), said now is the time to take action.
“The earlier we do it, the less duration and the less restrictive those measures will have to be,” he told Newstalk.
The rate of Covid-19 cases has gone up in four or five counties to almost the same level as Dublin and action is required now, he added.
“Unfortunately, if the number of cases continues to rise, whether in Dublin or in those counties, then unfortunately the only sensible thing to do is to go up to Level Four or even Level Five.”
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Dublin continues to have the highest incidence rate of coronavirus in the country, with the numbers expected to continue rising over the coming days.
The infection rate in the county now stands at 138 cases per 100,000 people over the last two weeks, almost double the national average at 70 cases per 100,000.
In Louth, the 14-day incidence rate of the disease now stands at 102 cases per 100,000 people. In counties Donegal and Waterford, the rate is at 97 and 94 cases respectively.
This comes after Dr Ronan Glynn, the acting chief medical officer, warned that Covid-19 is spreading "disproportionately" among younger people.
The latest figures from the Health Protection Surveillance Centre show 40 per cent of cases in the last two months have been in people aged between 15 and 34.
Another 334 cases of the virus were reported across the country on Tuesday.
NPHET will consider whether to recommend further restrictions at a meeting on Thursday.
