The Welsh Government could adopt an experimental app to track and trace coronavirus, the First Minister Mark Drakeford said.
The app is being trialled in the Isle of Wight this week.
Mr Drakeford said there are "advantages" to the software if issues with the app, such as the sharing personal data, could be solved.
His chief medical officer said the public will be willing to lose some freedoms to tackle the virus.
Ministers' in Wales want to track, trace and isolate coronavirus as a part of its plans to ease the lockdown
Dr Atherton said contact tracing would be a mixture "of old-fashioned public health track and trace together with some of the new digital technologies".
On Monday a draft UK government plan to ease restrictions, seen by the BBC, suggested reducing hot-desking and minimising numbers using equipment, as potential measures.
Lockdown powers are devolved, however, with the UK government having responsibility for England. The first minister, who is in charge of the lockdown in Wales, said he was in "broad agreement" with the plan.
A trial of an NHS app, led by UK government body NHSX and aimed at limiting the spread of the virus, is to begin on the Isle of Wight this week.
Using Bluetooth, the free smartphone app will track when its users come into contact with each other, automating the tracing process.
Epidemiologists have said about 56% of the UK population - equating to about 80% of smartphone owners - need to use the app in order to suppress the virus.
Contact tracing is not new and has been used in previous epidemics to control their spread - it was used for coronavirus earlier in the outbreak.
It works by helping identify people who have been in contact with someone who has had the virus, so they can isolate from others.
But there are concerns at the privacy implications of apps that gather data on large numbers of people.
Public Health Wales has produced a draft plan on how surveillance could work, which is currently being considered by ministers.
It is likely teams of people would be needed to implement the plans.
"At the moment we are working with the UK government on that app to see if we could make use of it here in Wales," Mr Drakeford told his daily press conference.
"There are issues to be worked through and that's why the Isle of Wight is being used as an experiment.
"Particularly issues to do with data, personal data, how that data can be shared, into the different health systems of England.
"If we can solve those issues that people would be willing to share their data I see advantages of being part of that wider app."
Asked if the public would and should be willing to part with personal freedoms to tackle the spread of coronavirus, Mr Drakeford gave a "conditional yes".
He said people in Wales "have always demonstrated a willingness to act collectively to do things in our own lives that have a benefit for others".
But the chief medical officer Dr Atherton said contact tracing with the current level of transmission of the virus in Wales would be "extraordinarily difficult".
"Certainly, there are trade offs to be made, in all of the decisions we make there are pros and cons," Dr Atherton said.
"You know, you have to ask yourself how much personal information would people be willing to put into this if it was able to start to tackle the coronavirus epidemic.
"By and large the sense that one gets from the communities [is] that some loss of personal freedom in terms of data would be worth doing for that.
"But that's something that we have to tread very carefully in the UK, of course."
"We're watching very closely what's happening in the Isle of Wight," he added, saying the trial was in its "very early days".
A review of the lockdown measures is required by this Thursday.
Asked if the Welsh Government would consider lifting restrictions on a region by region basis, Dr Atherton said he doubted it.
"I think that would be very difficult, not least because people move between areas," he said, suggesting that it would be more likely to be done on a "restriction-by-restriction" basis.
Commenting on the UK government's draft plan, Mr Drakeford said: "We are broadly in agreement with many of the proposals."
Mr Drakeford said in some ways Wales was in a "better position" because rules requiring firms to allow two metres between employees had already been introduced in Wales.