Backing for Kenny soccer fund plan
New hospitals for youngsters are planned in the two cities and are expected to cost more than £600 million.
The Taoiseach's proposal during a meeting in Armagh received support from political leaders north and south of the border, although t he head of Northern Ireland's governing Irish Football Association (IFA) said it was a "difficult proposition".
Mr Kenny said: "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.
"It would be a gesture from the sports people that would have a profound impact."
It included incoming Irish manager Martin O'Neill, Pat Jennings and Johnny Giles. Brazil won 4-3 in a match played at the height of the conflict in Northern Ireland, intended as a gesture of friendship.
Forty years later Mr Kenny attended a conference today on sport boosting reconciliation in Northern Ireland, organised by the codes of rugby, soccer and Gaelic Games.
He said a soccer game against England could be held at Belfast's Windsor Park or Dublin's Aviva Stadium. The Taoiseach earlier mooted Croke Park, the Dublin home of the Gaelic Athletic Association, as a possible venue.
Later, at a meeting of ministers from Northern Ireland and the Republic of Ireland, Stormont's Democratic Unionist First Minister Peter Robinson said the idea was a matter for the governing bodies of soccer to explore.
"As long as I am not the referee I don't mind being there. It doesn't threaten the autonomy or authority of either organisation for a charity match to be held for what would be a very good cause for young children in terms of hospitals both in Northern Ireland and in the south," he said.
"The proposal is something that would be supported. I said (to the Taoiseach), 'is there any chance I could play in goals?'," he joked.
Mr Kenny also suggested he and his deputy, Tanaiste Eamon Gilmore, could join Mr Robinson and Mr McGuinness in attending a variety of sports events in Belfast and Dublin to demonstrate their support.
IFA president Jim Shaw said an England game could be achieved if the desire was there.
"There is no objection to it. It would be very difficult to organise it, to get these sort of players from the two associations."
Ireland's new children's hospital is being built at St James's, Dublin, at a cost of more than 484 million euro (£404 million) and is planned to open as late as spring 2018.
A total of 200 million euro (£167 million) from the sale of the national lottery licence will part-fund the long-awaited development.
Conditions at the existing children's hospital in Northern Ireland, at the Royal in west Belfast, have been described as shocking. It is to be replaced by a state-of-the-art facility.
The UK Department of Health believes the final bill will be £250 million.