Taoiseach Enda Kenny and Northern Ireland Deputy First Minister Martin McGuinness have said they would like to see one football team represent the island of Ireland.
Mr Kenny said it is unwise to mix sport and politics, but as a football fan he would support having the same system as in rugby or boxing.
"I think they could certainly qualify for World Cups, we'd have a much stronger team. But then, I'm not in control of that," he said.
"When we do so much work... as we do in rugby, as we do in boxing, as our sports people in many spheres reach world-class performances and astride on the European stage, with achievements that are outstanding from my point of view personally, I'd be a big supporter of it."
Sinn Fein's Mr McGuinness, who is widely expected to meet the Queen as she marks her jubilee year, gave his backing to the idea during a meeting of senior north-south political figures in Dublin.
"I agree with the Taoiseach, and it's not a political point. I believe on the world stage, football-wise, we would be much more effective players if we were able to choose from an island of six million people," he said.
"I come from a part of the island where young men take decisions to play for the Republic, but also to play for NI, and it's terribly wrong for anybody to utter any word of criticism they make about their footballing careers. My attitude is if a team is playing in green, I will support them."
First Minister Peter Robinson declined to declare support for a single team: "I think everybody knows the direction I would want to travel, but let's not make political issues about sporting matters, let's just encourage local people who are involved in sport."
At present, football on the island is governed by two bodies - the Football Association of Ireland in the Republic and the Irish Football Association (IFA) in Northern Ireland.
Relations have been stretched in recent years over the number of young players from the north who declare for the Republic. The IFA has said it is upset after supporting and nurturing young talent, only for players to opt into another jurisdiction when they become seniors.