The Department of Justice is considering stricter rules so they know where people arriving into the country are self-isolating.
Figures for a six-day period between the end of April and start of May show almost 700 Dublin Airport passengers didn't leave their details with officials.
A third of follow-up calls to people who'd recently arrived here also went unanswered.
Currently, passengers are asked to fill out a form once they've landed but it's not mandatory.
Aviation analyst Alex Macheras says most countries have stricter rules than we do:
