Kenny mooted an idea than an all-Ireland team should face England every two years to raise money for children's charities.
Kenny was speaking in Armagh City at a conference on sport boosting reconciliation in Northern Ireland.
He said fixtures could be arranged for Wembley or the GAA's headquarters at Croke Park in Dublin.
The money raised would help fund research and facilities at specialist hospitals in Belfast and Dublin.
Kenny said: "Wouldn't it be a wonderful thing if we could have an all-Ireland soccer team playing England, perhaps on a bi-annual basis.
"The purpose of this would be the development of research and the development of both children's hospitals on the island of Ireland.
"It would be a gesture from the sports people that would have a profound impact.
"We could take on the might of England entirely for charity. It is just a thought, it might be something that could become a reality."
However, Patrick Nelson, chief executive of the Irish FA, said there was no appetite in his organisation for such a team.
Nelson added: "That's not going to be something that is on our radar. It has not been in the past and it won't be in the future."