The Taoiseach and Tánaiste are in Edinburgh for a British-Irish Council meeting, where they will hold informal government formation talks on the sidelines of the event.
Heads of government from Britain and Ireland will attend the gathering, which was established under the Good Friday Agreement.
Ministers from the Isle of Man, Jersey and Guernsey are also attending.
Micheál Martin and Simon Harris are due to hold informal discussions on the formation of a government here while they are in Scotland.
Fianna Fáil won 48 seats in the general election, while Fine Gael claimed 38, making another coalition involving the parties all but certain.
They need two more seats for a majority, and are likely to turn to Independent TDs rather than seeking a deal with the Labour Party or Social Democrats.
Issues to decide will include whether there will be a rotating Taoiseach, and how many ministers and junior ministers each party will have.
Fianna Fáil will look for a longer stint for Mr Martin as Taoiseach, rather than a 50:50 split, The Irish Times reports.
Others present at the British-Irish council meeting will include UK prime minister Sir Keir Starmer, Northern Ireland First Minister Michelle O'Neill, Scotland's first minister John Swinney and Welsh first minister Eluned Morgan.
