Former GAA president Nickey Brennan has urged Leinster counties to travel west to play Galway in the hurling championship.
He has also called on Leinster to welcome Galway's minors and U-21s into the eastern campaign, a request rejected last year.
"My view is that for championship purposes, Galway should be fully integrated into Leinster in all grades. I also think that counties should be prepared to enter home-and-away arrangements with Galway, similar to what's happening among Leinster counties now," said Brennan.
Despite playing in the Leinster senior championship for seven seasons, Galway have had no 'home' game. They travelled to Croke Park to play Dublin last Sunday, but the replay will stay in Leinster when the sides clash in Tullamore on Saturday.
"In all fairness, Galway are entitled to some home games. They have a good facility in Pearse Stadium. Players and supporters deserve to have championship games there as part of a home-and-away rota," said Brennan.
The Leinster Council is amenable to that arrangement but, so far, no Leinster county has agreed to enter a deal with Galway. That has fuelled suspicions in Galway that there's a tacit agreement among counties not play Leinster games across the Shannon.
Leinster counties have also rejected a request from Galway for inclusion in their underage championships.
"We're talking about the good of hurling here. Nobody can deny that Galway seniors playing in Leinster is good for everyone.
"But if it's to work properly, Galway should get some home games. And their minors and U-21s should be welcomed into Leinster," said Brennan.
The former Kilkenny player and manager was one of the driving forces behind the move to bring Galway seniors east during his term as Leinster Council chairman.
It came to fruition in 2009, two months after his term as GAA president ended.
He believes that the hurling championship formats are working well, but acknowledges that Galway have a grievance over home games.
"I would like to see Leinster counties move on this. It's about being fair to Galway and fully integrating them into the Leinster Championships," said Brennan.