Taoiseach Enda Kenny and British Prime Minister David Cameron have raised the possibility of a state visit to Britain by President Michael D Higgins following the Queen's historic trip to Ireland.
It would be the first full visit by an Irish president to Britain, although it is understood no formal moves are yet underway.
It is usually normal practice for a return invitation to be issued, although the format of the trip can vary.
Irish presidents have paid visits to the queen in the past -- like when Mary Robinson had tea in Buckingham Palace in 1996 -- but there has yet to be a full state visit.
It is a matter for both British and Irish governments to co-ordinate any visit, but Britain would have to extend an invitation first.
In the RTE documentary, 'The Queen's Speech', which aired last night, Mr Cameron said a visit by Mr Higgins would be a "great idea".
"We have now what ought to be proper, normal relations between two states and so we should be doing state visits with each other," he said.
"But the great thing about the British-Irish relationship is there's nothing normal about it, it is much closer than normal.
"There are these great bonds and common interests in language and culture and so many things that we share. And I can imagine a state visit, what we call an incoming, an inward visit from an Irish president."
Mr Kenny said he is sure a visit by Mr Higgins would happen "after an appropriate lapse of time". "I think it would be looked forward to by the million Irish people living in Great Britain with great interest," the Taoiseach said.
Mr Cameron also described the Queen's Irish visit as a "gamechanger". He said a strong relationship between Ireland and Britain already existed, and that it was "becoming warmer and more positive because of the settling down of the Northern Irish issue".