The chief minister believes whoever becomes the next UK prime minister will attend a high-level summit in Guernsey in June.
The British-Irish Council will focus on several topics including the economy and renewable energy.
Deputy Lyndon Trott said there was a belief it was likely as it would be the first council of their term.
Gordon Brown attended the council in July 2007, only a month after he became Prime Minister.
It was the last time a leader of the British government attended.
The council, otherwise known as the Council of the Isles, had its inaugural meeting on 17 December 1999 after it was established under the Good Friday Agreement.
It is a forum for discussing matters of mutual interest to the devolved administrations in Scotland, Wales and Northern Ireland, along with the governments in Westminster, Dublin, the Channel Islands and the Isle of Man.
The last summit held in Guernsey was in November 2004.