The GAA's Commercial Director Peter McKenna believes that All Ireland Championships being played behind closed doors remain a last resort.
The Championships are scheduled to get underway in October.
Progress to phase-4 of the country's reopening has been postponed by the Government.
That means it will be late August at the earliest by the time a crowd in excess of 200 will be allowed to gather outdoors.
The Taoiseach Micheal Martin said on Wednesday, "The concern about the rise in the number of cases over recent weeks is very real.
"The 'R' number, which we have all become familiar with, has now risen above '1' in this country."
He added, "The priority now must be to get that 'R' number back below ‘1’."
"Obviously the 200 limit is still continuing and that would make a huge challenge," Peter McKenna told RTE today, "But I’d be hopeful that we are responding very well as a nation to what NPHET are putting down.
"I think once you start to unravel the restrictions you will see slightly bigger crowds within the stadium. At two metres distancing we are probably at around 7,000 capacity within the stadium. That is very, very small really.
"At one metre we are probably at around 22,000 and if we are allowed a degree of brush off – by which I mean people walking by each other in the same row – we could probably get up to 28,000.
"You’d be hopeful that come October we might be allowed 30% or 40% capacity in the stadium. But it is very much dependent on where NPHET see our progress as a nation."
GAA president John Horan told The Sunday Game in May, "I don’t think behind closed doors is going to happen to be honest with you.
"I think if there is games to be on the pitch of contact sport, there is going to be a certain acceptance there will be crowds in the stadium. I think is where it is going to rest."
McKenna - who also serves as Croke Park's stadium director - told RTE, "I think it is the least preferential.
"The thing about our games is they are very much about crowd being there and enjoying it. That is why the club championships have started first.
"Okay, they are restricted to 200 people. In small villages that will accommodate them but when you look at some of the bigger clubs in some of the cities, that is going to be a challenge.
"I’d hate for it to be behind closed doors, but if the championship starts, I guess we’ll need to finish it.
"We’d like to finish it this year if we could. The preference would be to not have it behind closed doors, but we will if necessary. It would very much be the last resort."
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