Public health expert Dr Gabriel Scally says he 'continues to be worried' about the different approaches to self-isolation rules in the UK and Ireland.
Dr Scally said the 14-day period of self-isolation for people arriving into both countries is "great", but he is concerned about how governments on either side of the Irish Sea are implementing the measure.
He's also warning that avoiding the risk of 'importing new cases' will be important when considering whether we can speed up the lifting of any restrictions.
People arriving in the UK from next week will be told to self-isolate for 14 days, but people travelling from Ireland are exempted from doing so.
However, there is no such exemption in place for people arriving here from Britain.
Speaking on Newstalk Breakfast, Dr Scally said it's vital that Ireland avoids the risk of importing new coronavirus cases as restrictions begin to be eased.
He said concerns remain about a potential 'Dublin dodge', where people travelling back to the UK from abroad would do so via an Irish airport in order to avoid self-isolation.
He explained: "There are a lot of voices in the UK who are calling for there not to be any quarantine of people coming in.
"While things are positive in Ireland as a whole - the North is doing well - in the UK they believe they are still getting up to 8,000 new cases per day."
Meanwhile, Dr Scally said if things continue to go well in Ireland there would be cause to consider bringing forward some of the plans to ease restrictions.
However, he also suggested it would be "wise" to see how things go in phase two first before making any decisions.
He explained: "It all depends on what the evidence is about the number of cases.
"That number is low, and it's getting lower. I was very pleased to see there were six counties where there were no new cases last week... that shows really great progress.
"Whether [things] should be speeded up or not, that depends on two things - how the number of new cases develops over the next week or so, and then importantly from my point of view that we avoid the risk of importing new cases i.e. passengers coming in through ports and airports."
