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 diagnosed and the total number of positive tests has reached 24,639.
Pride Of A County - Comeback Kings Wicklow Overcome 12-Point Mountain To End Wait For National Glory
"We Don't Know When We're Beat": Wicklow's Miracle at Croke Park as the Garden County beat favourites Down in thrilling, extraordinary fightback
No Changes To Starting Team As Wicklow Football Yearns For Historic Croker Triumph
Wicklow name unchanged team for Tailteann Cup final against Down
Wicklow Braced Once More As Coillte Signal Orange Fire Warning
Public is warned against fires or barbecues in forests or recreational areas, no blocking of emergency access routes, extra vigilance around dry vegetation
Wicklow Boss Targets Tailteann Cup Glory As Down Challenge Looms At Croke Park
'It's not worth a big pile unless we actually go and win it' says the positive Wicklow boss
Wicklow TD Calls For Straw Incorporation Funding For Struggling Tillage farmers
Brian Brennan presses Government for a decision on the Straw Incorporation Measure for struggling tillage sector
8:00pm - 10:00pm
Love Songs on the Coast
Sunny
High: 21°C | Low: 14°C
Sunny
High: 20°C | Low: 14°C
Sunny
High: 22°C | Low: 13°C
Sunny
High: 23°C | Low: 12°C
Sunny intervals
High: 26°C | Low: 12°C