The Health Minister Vaughan Gething said we may be able to move at a "slightly faster rate" when it comes to easing lockdown restrictions.
Mr Gething said we are in this position because people in Wales have followed the rules.
Last week, Boris Johnson announced that people in England who live alone would be able to form a "support bubble" with one other household. This means that single grandparents have been able to hug their grandchildren for the first time in months and couples have been reunited. The rule currently applies for England-only.
Mr Gething said the Prime Minister's decision took the Welsh Government by surprise. He said: "We have yet to see the evidence that underpins that. We know it was a successful help in New Zealand but it comes from upsides and downsides.
"Our scientific advisors are looking at that evidence so we're considering the position. We've already signalled we need to take a limited number of major interventions in each period of time."
Mr Gething said the guidance on staying local is still an important part of keeping Wales safe. He has not confirmed whether the 5-mile rule will be extended to allow longer journeys.
He said: "We want to move out of lockdown as fast as possible but as safely as possible. We've had good evidence this week that we're still seeing a fall in coronavirus and that does give us some room for manoeuvre.
"We need to balance all these things up because we'd like to see non-essential retail open, we know that we're going to see schools reopening in some form at the end of this month too so we have to think what else is possible to do over this next period."
The First Minister Mark Drakeford will announce changes to the lockdown in Wales at the end of next week.