He suggested bringing Northern Ireland and Republic players together under one banner for the clashes, which could be played at Wembley in London or at Croke Park in Dublin.
Mr Kenny said the money raised could be donated to hospitals across the island of Ireland.
"We could take on the might of England entirely for charity, for the children's hospitals (of Belfast and Dublin), for the children of the island, for research and development of what can impact on their little lives," said the Taoiseach.
"It is just a thought, it might be something that could become a reality."
The idea was raised at a conference in Armagh City on how sport can contribute to reconciliation in Northern Ireland on Friday.
Representatives from football, rugby and GAA attended.
Back in 1973 a squad of NI and Republic players took on Brazil, losing 4-3 in a match which was played as a gesture of friendship during some of the hardest years of the Troubles.
Irish Football Association president Jim Shaw said organising an all-Ireland v England game would be challenging - but believes it could be done.
Mr Shaw said: "There is no objection to it. It would be very difficult to organise it, to get these sorts of players from the two associations. It is a difficult proposition, but I am sure at some level it can be achieved if the desire is there."
However, on Friday evening, the IFA released a statement "to clarify that the idea is not, and will not be on the Association's radar."