O'Neill and GPA chief executive Dessie Farrell met with Irish Sports Council (ISC) chairman John Treacy and GAA President Sean Kelly on Wednesday in the latest round of discussions over the proposal.
O'Neill is now hoping that the GAA, GPA and ISC can sit down for discussions with the Departments of Sport and Finance sometime in the New Year which would take the issue forward.
Both the Minister for Finance and for Sport have already reacted positively to the idea while GAA President Sean Kelly is also keen to see how far the matter can be taken, according to O'Neill.
"The feedback from the GAA has been very positive," he said. "This is something that suits both our objectives. It wouldn't put them in a position where it flaunts their regulations and they wouldn't have to put their hands in their pockets."
Indeed, the scheme wouldn't cost the GAA a penny. The players' group is proposing that the money should come from the Irish Exchequer.
"The money would be issued to the Irish Sports Council, who would give to the GAA and they would distribute the grants to all the players, including those in the six counties," said O'Neill.
In the initial draft plan, there would be three levels of funding €2,500 for tier one, €1,750 for tier two, and €1,000 for tier three. In hurling that would break down into the Liam McCarthy, Christy Ring and Nicky Rackard Cups.
"In football, it would be based on the extent of a player's involvement in the championship. First round qualifier knock-outs would get the lowest sum, while the top 12 teams would take receipt of €2,500," explained O'Neill.
Based on 63 inter-county panels (Kilkenny do not field a football team in the championship), the total annual cost to the Exchequer would be approximately €3.6m "a drop in the ocean for the Government," claimed O'Neill.
The GPA director revealed that players would receive the grants on the grounds that they are preserving an important aspect of Irish culture and heritage.
"The Irish government has an artist's programme in which about 300 artists are supported for their perceived contribution to Irish culture. The sports minister John O'Donoghue has said the grant could be defined in this manner.
The GPA's initial proposal that sought tax breaks for GAA players was debated in the Dáil last March and defeated despite initial support from 121 TDs. O'Neill is hopeful that the latest idea could come to fruition but said that discussions "have stalled on the doorstep".
And the Armagh native insisted that the GAA must start thinking about a long-term plan about how it will support players if it wants to avoid a total catastrophe.
"When Croke Park starts hosting the rugby and soccer internationals the GAA is going to have €30 million coming in from those extra games. Meanwhile players will be operating in this vacuous state where the GAA is turning over €150-200 million while a house in Dublin will cost €700,000.
"There seems to be a reticence within the GAA to look seven to 10 years down the line. The GAA needs to look beyond presidential terms and look long term.
"I've looked at all the other codes and examined how and why they went professional.
"We are exactly where everyone else has been and history will only repeat itself."
Interestingly, O'Neill paid tribute to current president Sean Kelly for the support he has given the current plan.
"It's unfortunate that he doesn't have another year or two. He has great confidence and authority on a whole lot of matters," he said.