The Department of Transport has told the Oireachtas Covid-19 committee that it is considering the measure.
The move follows criticism of a current lack of diagnostic checks at ports and airports.
Ken Spratt, from the department, says stricter measures may be brought in for international passengers:
“It is the case that we do believe there is more that could be done, and we’re giving consideration to potentially introducing testing – departure point testing, and also some testing is already in place in Dublin Airport, particularly where a person with symptoms is presenting.
We are considering what additional measures we could and perhaps should introduce.”
The proposal means that passengers may have to get tested for Covid-19 before being allowed to travel abroad.
If a passenger were to test positive for the virus, they would then not be permitted to leave the country.
The proposal comes after the Government’s launching of a “green list” of 15 countries, from which people may travel to and from without self-isolating for 14 days upon arrival in the Republic.