The Government is considering lifting the travel limit and a number of other lockdown restrictions three weeks earlier than planned.
The 5km rule, which is set to be extended to 20km on June 8, could be scrapped altogether by Phase Three on June 29.
Hairdressers, museums, galleries and swimming pools could all also reopen at the beginning of Phase Three.
Both Taoiseach Leo Varadkar and Chief Medical Officer Dr Tony Holohan have acknowledged that fast-forwarding Ireland's 'roadmap' to recovery was possibly.
But it will entirely depend on the number of Covid-19 deaths, new cases and ICU admissions in the next few weeks.
The Government has been coming under increased pressure from business lobby groups to let many organisations reopen earlier - by reducing the current 2m social distancing rule down to 1m.
And now, senior Government sources have confirmed that moving up the timeline for reopening many amenities is being considered, the Sunday Independent reports.
Meanwhile, Dr Tony Holohan said he would like to see Ireland’s re-opening accelerated – if the progress of the virus allows.
After Taoiseach Leo Varadkar said the majority of people wanted the pace of change to speed up, Dr Holohan told the Irish Mirror: “People would like to see things happening as quickly as possible and I would be one of them.
“It sounds like an expression of what we would all like to see.
“If the evidence or experience of other countries changes our assessment as to when something might be recommended at a different point, then we would make that advice available.”
It comes after NPHET's Dr Philip Nolan said the outbreak in Ireland remains “astonishingly stable”.
