Former president of the GAA Sean Kelly has said it is "a pity" that the Liam Miller testimonial cannot take place in Páirc Uí Chaoimh.
Mr Kelly was at the helm of the organisation when it took the historic decision to open Croke Park to rugby and soccer.
Fianna Fáil has written to Croke Park seeking a change of heart on the decision so that Páirc Ui Chaoimh is made available for the testimonial.
It emerged this week that a request was made to play the fundraiser for the late footballer's family at the revamped home of Cork hurling and football, which has a 45,000 capacity.
The Cork County Board was open to the idea, but was unable to open the doors as GAA rules do not allow soccer or rugby to be played on any of their grounds bar Croke Park.
Mr Kelly said: "The rules need to be changed to reflect grassroots feelings. There will be occasional times when we have to show generosity and the rules have to be changed to allow for this."
A host of well-known soccer stars from home and abroad, including Roy Keane and Rio Ferdinand, have signed up to play in the testimonial, which is due to take place at Turner’s Cross on 25 September.
The 7,000 tickets sold out in hours and this will no doubt lead to further calls for the GAA to open the doors to Páirc Uí Chaoimh.
However, Croke Park officials say that they cannot change their rules without going to Annual Congress, which will not meet again until February 2019.
Mr Kelly's comments come as a number of political figures have thrown their weight behind calls for the game to be played in Páirc Uí Chaoimh.
Fine Gael Senator and ardent Cork GAA fan Jerry Buttimer tweeted that he hopes a way can be found for the testimonial to be played in Páirc Uí Chaoimh.
Mr Buttimer, who is the leader of the Seanad, added: "Those who are quick to comment should recognise that the GAA has an official rule book. But this is an exceptional case."
Earlier today, the Fianna Fáil leader Micheál Martin tweeted: "The GAA is rooted in community. Liam Miller and family are of our community. Páirc Uí Chaoimh underpinned by our community. The unique event organised to reflect that community ethos and to honour Liam Miller should be held in Páirc Uí Chaoimh."
His party colleagues, Cork North West TD Michael Moynihan and South Central TD Michael McGrath have also adopted a similar tone.
Mr McGrath claimed GAA headquarters has "missed a golden opportunity by not opening the doors of Páirc Uí Chaoimh for the Liam Miller tribute match.
Fianna Fáil’s spokesperson on Sport Kevin O’Keeffe has written to the GAA President John Horan requesting that Páirc Uí Chaoimh is made available for the testimonial.
He said: "It disappointed me, as a lifelong supporter of gaelic games, that the request for the testimonial to take place in Cork’s premier sporting facility was rejected by GAA Headquarters.
"Liam Miller played soccer with distinction for his country, but in his youth was a proud GAA footballer.
"His untimely death cut short a very promising career and has left his family heartbroken."
He said the GAA is entitled to decide who uses its facilities.
But he said he finds it "hypocritical and disingenuous for Páirc Uí Chaoimh and other sporting facilities to be used as venues for music concerts, and in the recent past, as venues for American Football."
"Remembering and recognising one of Cork’s sporting stars following his untimely death is something ordinary, decent members of the GAA undoubtedly support," he said.
The Cork East TD added: "Ireland and its people have long moved past disagreements between GAA and soccer people. We all share and revel in the successes of all Irish people playing sport."
Sinn Féin TD Jonathan OBrien claimed many GAA members are disgusted by the organisation’s statement on the matter and said "the decision doesn't reflect the ethos of the GAA, an ethos of community and giving back."
He accused the organisation of showing no empathy.
