Stay at home rules banning all but essential travel could be eased when Wales' Covid regulations are reviewed.
First Minister Mark Drakeford said guidance could be changed to "stay local" as part of moves to "restore more freedoms".
"I think there is a case for an intermediate step between stay at home and being able to travel anywhere across Wales," he said.
A review of lockdown measures is due to be announced on Friday.
Wales went into lockdown on 20 December following a spike cases.
Since then the case rate, which measures the number of Covid infections per 100,000 people over a seven-day period, has fallen to an all-Wales average of 46, down from 437 in the run up to Christmas.
And almost one million people have received their first dose of the Covid vaccine in Wales.
"So, that is what we will be trying to make happen on Friday of this week.
"We will be looking carefully this week at whether an intermediate period of stay local - people are used to that, we had a period of that last year in Wales - whether that would be a first step on a journey.
"Remembering that in Wales that is how we are trying to approach the whole business - carefully, cautiously, step by step, not doing too many things at once - so that we can monitor the impact of changes, and then restore more freedoms to people and to the economy once we are confident that it's safe to do so."
Plaid Cymru leader Adam Price has previously said there should be a "careful" approach to easing restrictions due to new Covid variants.
The Conservative leader in the Senedd Andrew RT Davies has called for a "clear roadmap out of lockdown".