Such a visit would have been unthinkable in the past due to the threat of Republican violence.
However, the visit is now being planned after a meeting between Prime Minister David Cameron and Irish Taoiseach Brian Cowen.
The Irish premier said he wanted to see the official engagement before Irish president Mary McAleese leaves office next year.
Mr Cowen said there was now no obstacle in the way of the Queen coming to Ireland.
"I think that would be a good development," the Taoiseach said.
"I think also that the importance of an exchange of state visits says a lot about the modern bilateral relationships we now have.
"We have started a process between both the prime ministers' offices whereby we can look at this prospect. I would like to see this happening during the tenure of our own president."
Mr Cowen, who met Mr Cameron for talks in Downing Street, said a state visit by the Queen, and a return trip to Britain by an Irish president, would be part of the normal courtesies enjoyed by friendly, neighbouring states.
Ms McAleese, who is known to have worked behind the scenes for a bridge-building visit, suggested the wheels were firmly in motion.
"Following today's meeting between the Taoiseach and Prime Minister Cameron in London, President McAleese looks forward to the prospect of a visit to Ireland by Queen Elizabeth in the near future," said her spokeswoman.