The Welsh Government has said that a proposed Basic Income (BI) trial could involve people leaving care.
Speaking to ITV Cymru's Rob Osborne, the First Minister was asked how 'universal' the trial would be.
Drakeford replied that any trial would have to be 'modest' and affordable, due to the limited powers of the Welsh Government.
He said: "What we are doing here is testing the concept. It will have to be a scale of pilot that we can manage and afford. And it will need to be sufficient for us to be able to test the claims that are made for Universal Basic Income. But it will be modest in scope inevitably because we don't have all the major levers you need in your hands as a government to do this on anything other than a pilot scale."
Basic Income Trial
Over the weekend, the First Minister told journalist Emma Grant that he was committed to trialling a Basic Income during his tenure.
Speaking to Grant, Drakeford said that he had a "very long-standing interest" in a Basic Income.
He said that the pilot needed to be "carefully designed" and would have to "draw on the experience of attempted pilots in Scotland."
A Basic Income pilot is one of specific responsibilities entrusted to the Welsh Government's new social justice minister Jane Hutt.
He also said that he would be willing to work on a "cross-party basis" to "design the best possible pilot that we can design for Wales."
Almost half of Senedd members are in favour of trialling a form of Basic Income.
Thirteen Labour MSs, eleven Plaid Cymru MSs, as well as the sole Liberal Democrat MS, party leader Jane Dodds, have already pledged their support for such a trial.
Reacting to the news, UBI Lab Cymru said: "Safe to say this is disappointing if true. To be as close to Universal as possible, the trial must include the employed, unemployed, children and pensioners."