Galway hurling manager Conor Hayes believes that Galway would benefit from playing in the Leinster Championship and has suggested the issue should be revisited.
The Tribesmen declined an invitation from Leinster officials to join their provincial competition last year, giving no official reason for their decision.
The qualifier system didn't seem to do them any harm this year as they impressively accounted for Limerick, Tipperary and Kilkenny en route to their eventual All-Ireland defeat to Cork.
However, speaking in today's Irish Independent, Hayes said he thought the county would benefit greatly from competing in Leinster.
He said: "We have absolutely nothing to lose and plenty to gain. I genuinely believe that Leinster's invitation to play in their championship should be looked at again.
"Even if we lost a first game in Leinster, we would still have the qualifiers. We would also have learned a fair bit from the first game.
"And if we got to a Leinster final, we would be guaranteed a place in the All-Ireland quarter-finals.
"Everybody could see how much we progressed as a team during this year's qualifiers. The extra games brought us on an awful lot and I believe that if we were in Leinster it would help us even more."
Leinster Council chief executive Michael Delaney says they won't be inviting Galway again and insisted the ball was firmly in their court.
He said: "We won't be going back to Galway to ask them in again because they made a decision to go it alone and we respect that.
"However, if Galway were to come to us, I'm sure they would be welcomed. The ball is in their court on this one. Leinster never withdrew the invitation."