Taoiseach Leo Varadkar said he could envisage a successor of his coming from the unionist tradition.
Mr Varadkar referenced the controversial decision by his predecessor John Bruton to display a portrait of John Redmond in his office when he became taoiseach in 1994.
Speaking at the launch of the book Judging Redmond and Carson by Prof Alvin Jackson, the Taoiseach said the "mature, inclusive way in which the Easter Rising was commemorated suggests we are moving away from such emotive reactions".
Mr Varadkar revealed he has a portrait of a Fianna Fáil taoiseach Seán Lemass in his office along with one of Michael Collins and a tribute to the Suffragette movement.
He added: "Perhaps it is not too far-fetched to imagine a day when a portrait of [Edward] Carson or [James] Craig may adorn the Taoiseach's office or the possibility that the office holder might hail from that tradition."
Mr Varadkar did not mention Sinn Féin president Mary Lou McDonald by name, but alluded to her tiocfaidh ár lá remarks at the end of her first speech as party leader.
He said: “Carson has often been described as a patriot not a nationalist and it reminds us there can also be nationalists who are not patriots.
‘Speak loudest’
“Sometimes people who speak loudest about how our day will come never provide details as to what kind of day will come or how it will be welcomed by other people.”
The launch of the book, which is published by the Royal Irish Academy (RIA), followed on from a day-long symposium on the Irish Parliamentary Party to mark the centenary of John Redmond's death.
The symposium was the official State commemoration for Redmond's death and was organised by the National University of Ireland (NUI); the Department of Culture, Heritage and the Gaeltacht; the Royal Irish Academy; and the school of history UCD.
Mr Varadkar suggested the Judging Redmond and Carson book represented a "more nuanced and mature approach to the conflicts that shaped the Irish state and the state of Northern Ireland as each approach their centenary.
“I think it is time to approach the past with empathy and a spirit of generosity and respect for the context in which decisions were made and not how we would have preferred things to have happened,” he said.
“I think if we approach the past with respect, tolerance and understanding we can approach our challenges in the present in the very same way too.”
Mr Bruton, who has been a long-time champion of Redmond, told a gathering in Westminster that there were many parallels between the negotiations surrounding Home Rule and Brexit.
Home Rule
The issue of whether or not Ireland would remain as part of the UK customs union in the Home Rule settlement was one that dominated discussions 100 years ago.
Unionists feared that tariffs between Ireland and Britain would cut northeast Ulster off from its base.
Mr Bruton said Redmond gave ground on the issue of customs posts as a concession to unionists, but the Anglo-Irish Treaty took the Irish Free State out of the UK customs union and Border posts were installed.
Mr Bruton was speaking at a meeting in Westminster organised by DUP MP Sir Jeffrey Donaldson and Down-born Labour MP Conor McGinn to mark the centenary of Redmond's death.
Redmond, Mr Bruton suggested, was a “better model for a 21st-century world than are those who did not accept the necessity for compromise, and who failed to make an adequate effort to understand the aspirations of their traditional opponents.
“When passions are inflamed, absolute demands backed by violence, are actually the easy way. No intellectual, or imaginative, effort is required. In these circumstances, compromise is harder, riskier, and more painful.”
