The Taoiseach has proposed the establishment of an all-island soccer team on a temporary basis for charity.
Speaking at a reconciliation through sport event in Armagh in Northern Ireland, Mr Kenny said the team could play England every two years.
He suggested funds raised could be used for the Children's hospitals in Belfast and Dublin.
"Wouldn't it be a wonderful thing? But you can't have an all-Ireland soccer team playing in international competitions," he said.
"But perhaps on a biannual basis there would be a charity match played in Ireland and England."
Ireland had a football team made up of players from the entire island from the late 1800s until 1950, when the Irish Football Association resolved itself into the two separate football associations we have today. The all-Ireland team won the championship in 1914.