Published Saturday, 16 June 2012
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The leaders spoke at a meeting of the North South Ministerial Council in Dublin.
Mr Kenny said he would like to see the system used by other sports such as rugby adopted by football, but cautioned that it is unwise to mix sport and politics.
"I'd be a big supporter of it," he said. "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."
Mr McGuinness also likes the idea.
The Sinn Féin politician said: "I agree with the Taoiseach, and it's not a political point.
My attitude is if a team is playing in green, I will support them.
"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.
"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 world of criticism they make about their footballing careers."
However First Minister Peter Robinson was less enthusiastic.
The DUP leader said: "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."
The right for players to pick which country they would like to represent was enshrined in the Good Friday Agreement and has been backed by governing body Fifa.
A number of high profile players have opted to declare for the Republic in recent years, including Darron Gibson and most recently James McClean.
Northern Ireland have not qualified for a major international tournament since the World Cup in 1986, while the Republic of Ireland were knocked out of Euro 2012 on Thursday after two defeats in the group phase to Croatia and holders Spain.
Both Mr Robinson and Mr McGuinness said the matter of a single team is one for the island's governing bodies - the Football Association of Ireland in the Republic and the Irish Football Association (IFA) in NI - to consider.