The daa wants passengers arriving in Ireland from non-green list countries to prove they have tested negative for Covid-19.
It believes they should be forced to take a test less than 72 hours before they arrive.
The company, which runs Dublin and Cork airports, will make the call at the Dáil's coronavirus committee today.
The committee's chairman, Michael McNamara, expects a number of other issues to be raised today.
"What can we do to open up tourism in a safe way, or can tourism be opened up in a safe manner, and what supports are necessary until such time as the country's in a position to open up more," he said,
"I would also expect maybe some questioning on the revelations over the weekend that the Government is obtaining data regarding passengers and using that to deprive them of pandemic payments."
Meanwhile, Ryanair claims 325,000 jobs in the tourism industry could be lost if the aviation industry does not recover.
The airline will tell the Dáil committee today passenger traffic is not likely to return to normal until 2024.
It will also say Ireland has the fifth-highest rate of coronavirus in Europe - much higher than many countries that are not on the 'green list'.