The first minister will promise to review restrictions on travel when he announces changes to Wales’ lockdown on Friday.
For the last few weeks people in Wales have been asked to “stay local” – with five miles from home given as a guide.
Mark Drakeford will now review the restriction by 6 July.
At the same announcement he will give the go-ahead for all shops to open from Monday, so long as they comply with social distancing rules.
The reopening of outdoor courts for non-contact sports, such as tennis, is also expected.
Mr Drakeford will set out the changes at a press conference at lunchtime.
Conservative politicians had criticised the five-mile guidance as unfair on people from rural areas, but the first minister said it was a “rule of thumb”.
One advisor to the chief medical officer has also called for a review.
It comes ahead of the reopening of schools on 29 June.
Lockdown in Wales is controlled by the Welsh Government, which has emphasised a cautious approach to lifting restrictions as case numbers have fallen.
The original stay-at-home legislation was dropped three weeks ago, when ministers changed the law to allow people to travel within a local area.
Five miles was given as guidance for how far people should travel, although that was not set in legislation.
It coincided with a loosening of restrictions allowing two households to meet outdoors.
The Welsh restrictions stand in contrast to the situation in England, where people are able to travel with no restrictions.
Welsh ministers are under pressure to go further and allow the tourism sector to open in some form for the summer.
On Thursday evening the Welsh Conservatives welcomed the move to reopen shops.
But Tory Senedd leader Paul Davies said it would be unfair to prevent retailers from opening immediately, and many will “go to the wall if they are forced to rely on local trade alone”.
He called for travel restrictions to be scrapped, for the property market to be reopened, and a timetable for the tourism sector.
Plaid Cymru said the Welsh Government should make clear what sectors are next.
Health spokesman Rhun ap Iorwerth called on the first minister “to relax restrictions as fast and as safely as possible and to consistently test and challenge the decisions they take as we move towards a new normality”.
But he warned the outbreak in his Ynys Mon constituency at a chicken processing plant “has shown that the threat of the coronavirus is still very, very real”.
Mark Drakeford asked retailers in Wales at the last lockdown review to prepare for a possible reopening.
After queues when shops in England reopened on Monday, Health Minister Vaughan Gething said he did not want to see large crowds outside reopened shops in Wales.
Retailers will be expected to follow social distancing laws which require firms to go as far as they can to keep people two metres apart.
Similar measures have already been in use in supermarkets and other retailers that have been allowed to remain open.