The Irish Catholic newspaper claimed the Archbishop of Dublin, Diarmuid Martin, had said he had discussed a visit with Pope Francis, and the Pontiff had said either he would come, or his successor would.
The Catholic World Meeting of Families is staged every three years in a different location around the world, and is usually attended by the Pope.
If the Pope comes to Ireland, it will be the first papal visit here since Pope St John Paul II in 1979.
It will not be Francis’s first visit, however, as he spent three months in Dublin in 1980 when, aged 43, he came to study at the Jesuit-run Milltown Institute.
The Irish Catholic has gone as far as to speculate where he may visit in 2018.
“It is expected that as well as visiting Dublin and the North, most probably Armagh, a papal visit to Ireland will include pilgrimages to one of Ireland’s historic monastic sites and to Knock Shrine, trips to Marian shrines being common features of papal visits,” it said.