Management at Dublin and Cork airports are looking to cut up to 1,000 jobs.
In a message to staff on Tuesday, daa chief executive Dalton Philips said passenger numbers at Irish airports are currently down 99% compared to the same time last year.
He also said the outlook for the rest of this year "remains bleak."
He said the "collapse" in passenger traffic this year is not just a 2020 issue and that "most commentators and analysts agree that the industry won’t see a return to 2019 passenger levels for several years to come."
Before the COVID-19 pandemic struck, Dublin Airport was set up to handle about 33 million passengers per year with 2.6 million passengers in Cork.
But the daa warned: "Traffic in 2021 could be as low as about 21 million passengers at Dublin and Cork airports next year, compared to 35.5 million passengers last year.
"This crisis is completely beyond our control, but its impact means that we are facing very significant financial losses for this year, and continued uncertainty in the medium term."
Mr Philips added: "We are looking at all options, but to give you a sense of the scale of the issue that we are facing, when Dublin and Cork airports last welcomed 21 million passengers per year, we had between 750 and 1,000 fewer employees in the business."
SIPTU trade union representatives have called for "urgent discussions" with the daa.
Organiser Neil McGowan said: "We will insist that any workers leaving the company as a result of redundancy must do so on a strictly voluntary and agreed basis and our focus will be to ensure that as many jobs possible are maintained in Dublin and Cork Airports."
"We have also requested that the company shares its detailed plans for each section in the airports to include how any new safety protocols will affect staff numbers.
"The announcement will be of great concern to our members at the airports and their families."
He added: "While there is a great deal of uncertainty in the aviation sector in general, it is clear that the COVID-19 crisis will result in the airport operating in a different manner to allow for social distancing and we need to agree with management the staffing numbers that will ensure staff and passenger safety.
"This may well result in more staff in certain areas than previously required."
"The industry will play an important part in the long-term recovery of the economy and, for this to happen, its workers need to be supported over the coming period."
Recent figures from the Irish Aviation Authority (IAA) showed air traffic fell by 85% in April due to the coronavirus pandemic.
A total of 14,907 flights were handled by the authority last month - as against 96,131 in April last year.
While commercial traffic at State airports was down by 90%, and trans-Atlantic traffic dropped by 83%.
Dublin Airport recorded just 2,067 flights, an 89.8% decrease, while Cork Airport traffic fell by 93.9% and Shannon saw a 79.8% decrease.
The IAA numbers include all flights, including cargo flights.