There are serious concerns over the high number of countries exempt from quarantine rules in the North.
It comes as Taoiseach Micheal Martin prepares to announce a list of destinations where Irish people can travel to without having to self-isolate on return.
However, the Government is facing accusations of mixed messaging as it is still advising against unnecessary foreign travel despite plans to produce the 'green list'.
People visiting from these countries will be exempt from the two-week self-isolating period required of most passengers arriving in Ireland.
It is expected the list will be fewer than 20 countries and be based on rates of infection.
However, 59 countries have been cleared for travel without quarantine to Northern Ireland where Sinn Fein shares power.
There are no restrictions on people moving from the North into the Republic.
Yesterday, a senior Government source said there was a need for "more cohesion" on North/south travel restrictions.
"There is a memorandum of understanding with Northern Ireland and we need to build on that," the source said.
"We need better cooperation North and south and we need people to be on the same page."
There were no new deaths from Covid-19 yesterday, however six new cases of the virus were diagnosed.
The European Centre for Disease Prevention and Control monitors the rate of Covid-19 infections per 100,000 people in 31 countries.
The 14-day cumulative number of Covid-19 cases per 100,000 in Ireland stood at 4.8 last night.
Eleven countries, including popular holiday destinations like Italy, Greece, Cyprus and Malta, had a lower rate of infections as per the latest figures.
The other countries with lower rates are Norway, Finland, Hungary, Estonia, Slovakia, Lithuania and Latvia.
The UK's number stood at 14.1 per 100,000 last night and would be highly unlikely to be included on any green list.
Meanwhile, other locations popular with holiday-makers like Portugal (46.1), Spain (18) and France (11.5) would not make it on the list.
Sinn Fein health spokeswoman Louise O'Reilly said the green list of approved travel destinations does not make any sense in light of current health guidance.
"The advice on travel is that the planes can take off - but you can't be on them," she said.
She was referring to the advice from the National Public Health Emergency Team (Nphet) that people should avoid all non-essential foreign travel, despite the readiness of ministers to produce a green list for travel.
She called for the island of Ireland to be treated as "one epidemiological unit" for the purpose of restricting the spread of Covid-19.
However, she resisted the suggestion that it would be unpatriotic for citizens from this jurisdiction to travel through Belfast to take advantage of the 59 destinations available through the UK list of travel-approved countries.
Ms O'Reilly said New Zealand had made maximum use of the strength of being an island in keeping Covid-19 at bay, but Ireland had not.
"At the moment the situation is the planes can take off, but people can't be on them. Dr Gabriel Scally is right, we should be regarding the island as one epidemiological unit."
Meanwhile, supermarkets have seen a number of Covid-19 outbreaks around the country as staff became infected with the virus, it emerged yesterday.
Fast food outlets are also among the workplaces where cases of the virus have been found. One of these outbreaks was at a fast food outlet in Kildare, but is now under control.
Acting chief medical officer Dr Ronan Glynn said as people return to work they need to remember to maintain physical distance with colleagues.
"People know their co-workers and can drop their guard," he warned.
He said he was not aware of any customers in shops getting the virus.
Over the past 14 days, a total of 270 new cases have been diagnosed. Seven in 10 of those diagnosed were aged under 45.
The new cases were spread across 20 counties. More than half were in Dublin, 10pc in Kildare and 6pc in Cork.
Elsewhere, the Irish Nurses and Midwives Organisation said 65pc of nurses who have recovered from Covid-19 are still experiencing post-viral fatigue.