People could be advised not to travel to the North from next week.
The Government is strongly considering the measure because of the different level of Covid 19 infection rates and restrictions.
Tánaiste Leo Varadkar told his party colleagues last night the advice may be introduced, but no final decision has been made.
Sinn Fein TD Pa Daly says it’s unrealistic.
Meanwhile, 269 new cases of Covid-19 were confirmed in the Republic last night, along with six more deaths.
The 14-day incidence rate for the disease has dropped to 105 per 100,000 people.
On the same day last week, it was 119.
Locally in Monaghan there were fewer than 5 cases recorded yesterday , with the incidence rate at 102.6.
In Cavan there were 6 cases, and their incidence rate is at 90.6