Former Donegal captain and All-Ireland winner Michael Murphy says he would keep the current format but tweak the competition’s “exhausting” schedule.
The first round of group stage matches took place on 18 May and the final is scheduled for 28 July.
For Derry, Galway, Roscommon and Louth, who had to go through the extra preliminary quarter-final, that could mean seven matches in the space of 10 weeks if they were to reach the decider.
Armagh, Dublin, Kerry and Donegal had a extra week of rest ahead of the quarter-finals on Saturday and Sunday after winning their respective groups.
“I would give another opportunity to the current system as it is, but we definitely need more breathing space between games,” Murphy told BBC Sport NI.
“It’s exhausting for fans, they want time to discuss and delve into the matches for a couple of days. That’s very quickly taken over by the week-to-week games.
“I can only imagine for players what it is like having to get yourself prepared. There is a lot of travel, logistics, overnight accommodation. Things like that.”