Dublin Airport has proposed developing a pre-departure COVID-19 test system for high-risk locations.
It said this would coincide with the introduction of the new European Union 'traffic light' system for travel.
It is also working with health experts to provide a testing centre at the airport.
The proposals have been outlined to Government departments and other key agencies.
It added that discussions are "ongoing."
"We support the adoption of a new EU 'traffic light' system, but it should also be accompanied by an EU testing protocol for travel," the airport said.
This would also include Cork Airport, as both are run by the daa.
Depending on talks, a pre-departure testing programme could be available from the middle of next month.
But any final decision on pre-flight testing would be made by the Government, not the airport company.
A daa spokesman told Newstalk: "We have been discussing a proposal for pre-departure testing with a number of Government departments and State agencies and these conversations are continuing.
"Under this daa proposal, passengers from high-risk locations could prove they have tested negative for coronavirus before travelling here, and similarly Irish outbound passengers could take a pre-departure test for any countries that require it for Irish originating traffic.
"Tests would be taken less than 72 hours before departure."
The spokesman said the daa has talked to "more than 20 potential specialist providers" which could operate a COVID-19 screening facility at Dublin and Cork Airports for pre-departure tests.
While they could also be taken at other accredited facilities.
He added the new airport-based facilities could be in place by mid-October when the new EU 'traffic light' framework is due to be introduced.
EU 'traffic light' system
The new colour code approach for EU travel will be based on newly notified cases during a 14-day period - and the percentage of positive tests from all tests carried out.
Green would mean the total number of new cases is less than 25 during a 14-day period, and the percentage of positive tests from all tests is less than 3%.
Orange means cases of less than 50 in 14 days, but the percentage of positive tests is 3% or more - or the total number of cases is between 25 and 150 but the percentage of positive tests is less than 3%.
And red is for an area where the total number of new cases is more than 50 during a 14-day period, and the percentage of positive tests is 3% or more - or the total number of newly notified cases is more than 150 per 100,000 in 14 days.
A grey colour would be used if there is "insufficient information available to assess the criteria", or that the number of tests carried out per 100,000 people is less than 250.
This will be based on weekly information supplied by EU member states to the European Centre for Disease Prevention and Control (ECDC).
They are also being asked to provide data at regional levels, so any measures can be targeted to those regions where they are "strictly necessary."
