The Government has been warned that a rush to ease restrictions could lead to a resurgence of Covid-19.
It has been reported the Government is considering scrapping the travel limit three weeks earlier than planned.
It is due to be extended to 20 kilometres from June 8 but might be dropped by the end of next month.
Public health expert Dr Gabriel Scally said speeding up the country's re-opening carries risks.
"For the benefit of us all, we need to get this right," he said.
"A rush to make up for all those weeks that we've been bottled up could lead us in the wrong direction and it could lead to a resurgence of this.
"We don't want to get back to announcing death tolls in the hundreds. We just don't want to get back there because that would lead to even more mayhem for all of us."
Government considering scrapping coronavirus travel restrictions three weeks early
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 there are 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.
Professor Mary Horgan, a consultant in infectious diseases at Cork University Hospital, says the travel restriction has served a purpose.
"It really, I presume, was brought in to limit the number of people a given person would interact with," she said.
"But that was in the big peak we saw in late March and early April, and we're well past that now.
"I think we're at the point of seeing what are the benefits and what are the risks of continuing a very narrow ability to travel."
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.