The Minister for Sport says that could be revised upwards depending on public health.
Crowds are expected to return to Croke Park after the August Bank Holiday weekend.
Up to 5,000 spectators are set to be permitted at large outdoor venues following roadmap recommendations from NPHET.
For smaller venues, up to 25 percent of capacity will be allowed, or 5,000 - whichever figure is lower.
The Cabinet will consider the recommendations today.
Minister Eamon Ryan is optimistic that the figure of 5,000 could be revised upwards for the All Ireland finals if there is progress during the easing of restrictions: