The First Minister has revealed he is "in discussions" with Cardiff Airport over testing passengers on arrival into Wales.
Speaking at Plenary on Tuesday, Mark Drakeford said they are seeing if "we can find a practical way in which airport testing itself could be carried out.”
He added there will still hurdles to overcome and the tests would not be mandatory.
"You can't require people to do these things; it's a matter of voluntary participation."
"Therefore, you have to spend a bit of time to make sure that, if you are able to provide tests at an airport, you can do it in a way that is effective, and those discussions with the airport authorities here in Cardiff are continuing,' Mr Drakeofrd said.
Travellers who have visited countries not included on the exemption list, even for a transit stop, must self-isolate for 14 days.
The two-week period of isolation starts on the date you enter Wales. However, if you spend time immediately beforehand somewhere else in the UK or in another place on the exempt list, then you can discount the time spent there off from the 14 days.
Around 30 countries offer airport Covid-19 tests, including Iceland where airport swabbing followed by a second test can cut quarantine from 14 to five days.
In Germany, airport test results can cut self-isolation to three days. Britain’s biggest airport, Heathrow, is proposing the same approach as Jersey and already has a test facility capable of 13,000 swabs a day.
So far, the UK authorities are not convinced and PM Boris Johnson has said airport Covid-19 testing can give a “false sense of security”.
Some experts say quarantine can never be eliminated for travel from high-risk areas, because two separate coronavirus tests several days apart are needed for accuracy.
There have been a further 110 cases of Covid-19 in Wales, bringing the total number of confirmed cases in the country to 19,681.
Public Health Wales said no further deaths had been reported.
The health minister issued a stark warning that Wales has just "weeks" to act in order to prevent a second national lockdown, following an overall rise in cases across the country and sharp increases in specific areas such as Caerphilly and Rhondda Cynon Taf.
Mr Gething also warned that there will be consequences for anyone deliberately flouting COVID rules.
"The rules are here for the benefit of all of us, and they apply to all of us," he said.