Home building could resume from April 5th as part of a phased return of construction.
The plan's being considered by government, however it's unlikely a decision will be made next week.
Case numbers, GP referrals and the R number will be among the factors considered ahead of any announcement.
Only social housing, due to be completed before the end of April, is continuing at present.
Meanwhile, the 5 kilometre travel limit could be expanded to 8 or 10 kilometres next month.