The 70-day, 8,000-mile torch relay will travel the length and breadth of the UK, starting on May 19, before it reaches the opening ceremony at the Olympic stadium on July 27.
Speaking ahead of his meeting with British Prime Minister David Cameron last night, Mr Kenny said he welcomed the idea of bringing the torch to Dublin.
"It would be exceptionally well received in Ireland here and you can rest assured that both governments, and we've spoken about this previously, will give full support to this if the International Olympic Council agreed to it," said Mr Kenny.
The London 2012 Organising Committee confirmed yesterday that it was in discussions with the OCI and the Irish Government to take the flame to Dublin.
"These discussions are at an early stage. No route has yet been discussed and this is something we will work up with the relevant authorities before further details are confirmed later this year," the statement said.
President of the OCI Pat Hickey started lobbying to have the flame brought to Dublin when London was announced as the games' venue in 2005.
A spokesman for the OCI said it would be appropriate as the Irish Olympic team comes from both sides of the Border. He said the Irish body was "cautiously optimistic" that it would either be carried or brought to Dublin for a symbolic visit of less than 24 hours.
A final decision on the matter will be made by the International Olympic Committee at a meeting in Durban, South Africa in the first week of July.