A new test being championed as "100% effective" is said to be able to determine whether people have been infected with coronavirus in the past.
The antibody test has recently has been approved by health officials in England and could be rolled out within weeks.
On Thursday, Number 10 said it would "certainly" be available on the NHS but commercial discussions with its developer are ongoing.
In the future, it could pave the way for people who have antibodies to be issued with a certificate showing their Covid-19 status and potential immunity.
The Prime Minister's official spokesman said: "We have talked about, in the future, the potential for some kind of health certificate related to whether or not you have antibodies.
"But we need a better understanding of how the immune system responds to the virus and the length and level of immunity following infection to better understand the potential of the test."
Though the test has not yet been given the green light in Wales, NHS Wales' chief executive said it's a "very positive development" for the Welsh Government's test, trace and protect strategy announced on Wednesday.
Speaking at a Welsh Government coronavirus briefing on Thursday, Dr Andrew Goodall said the accuracy of the testing regime needs to be validated and then a commercial arrangement would need to be sorted before the test became available.
He said officials in Wales will be involved in discussions this on Thursday afternoon and will make an announcement in due course.
"Hopefully we can take advantage of a UK deal in place for that if it comes through," he said.
Here's everything you need to know about the test
How does it work?
The test involves taking a small sample of blood and testing it for antibodies which will indicate exposure to coronavirus.
How reliable is it?
The test is said to pick up 100% of people who have had coronavirus.
It also has a specificity of over 99.8% - meaning it picks up virtually all people who have not had coronavirus.
A test that is 100% specific means all healthy individuals are correctly identified as healthy - there are no false positives.
Public Health England (PHE) has evaluated the new test, developed by Swiss pharmaceutical giant Roche, and has approved it as being safe and reliable for widespread use.
What if I've never had any symptoms of Covid-19?
This will not affect the test.
Experts believe a proportion of people who have had Covid-19 never actually develop symptoms.
The new test can identify people who have had coronavirus even if they have never had any indication they are infected.
If I've had coronavirus, am I now immune to it?
Scientists are unsure whether the test guarantees immunity to the disease.
Experts believe that while the presence of antibodies indicates a level of immunity, it is unclear whether people are completely protected and how long any immunity lasts.
Who will be able to get the test?
The UK Government said it plans to first roll out the test to front-line workers such as those in health and social care.
However, it is hoped the test will eventually become available to the wider public.
Roche claims it will be able to provide hundreds of thousands of antibody tests to the UK every single week.
