The Government is considering scrapping the Covid-19 travel restriction three weeks earlier than planned.
Other measures like the re-opening of museums and hairdressers could also be brought forward.
Phase Two of the country re-opening is due to start on June 8.
That will see more shops re-opening and larger numbers allowed at funerals.
The travel limit is also set to be extended from five kilometres to 20 kilometres from someone's home.
That is due to stay in place into Phase Three on June 29.
But the Sunday Independent reports the government is looking at scrapping that restriction at the end of Phase Two.
Museums, galleries and hairdressers being allowed to open by the end of June is also under consideration.
The Government has said speeding up the roadmap can only happen if the pattern of coronavirus continues heading in the right direction.
The latest figures show a further nine people with Covid-19 have died, bringing the death toll to 1,651.
There are also 59 new cases - with the total now standing at 24,929.
