The government will consider accelerating the lifting of restrictions if the number of new cases continues to decline.
Some aspects of phase 4 on July 20th could be brought forward to phase 3 on June 29th.
The Irish Times' report comes after another four people with coronavirus died in the Republic, bringing the death toll to 1,608.
57 new cases have been confirmed and the total number of positive tests has reached 24,639.
UCC professor Gerry Kileen says the current approach to flatten the curve before the virus is eliminated isn't the way forward.
"We need to decide whether we are out to eliminate this virus, and get ourselves into a position where we can really lift restrictions properly.
"But at the moment our current strategy seems to based around flattening the curve, and living with the virus over the long term, which for me is really the wrong choice."