I was asked about filling top EU post, confirms Taoiseach
Mr Kenny revealed that the approach was made prior to the annual congress of the European Peoples's Party (EPP), of which Fine Gael is a member.
He indicated that he was asked to consider running for the Presidency of the European Commission, which is currently held by Portugal's Jose Manuel Barroso.
But Mr Kenny insisted that he is instead giving his full support to the EPP candidate for the post, Jean-Claude Juncker.
"In respect of the presidency of the commission, from an EPP-wide view, we've had a congress, a contest, a vote and a candidate. That's the official position and we support Jean-Claude Juncker in that regard," Mr Kenny said.
"There were comments said to me, prior to the congress in Dublin; that issue is now irrelevant."
The Taoiseach was speaking at a joint press conference in Government Buildings last night with Dutch Prime Minister Mark Rutte, who travelled to Dublin to discuss Mr Juncker's candidacy – which has been the subject of major controversy.
But Mr Kenny last night rowed in behind German Chancellor Angela Merkel and pledged his support for Mr Juncker.
However, his admission that he was approached for the position himself illustrates the divisions within political circles over Mr Juncker's candidacy.
Mr Kenny has previously said he was "flattered" at reports that he was being considered. He has also been linked to the position of president of the powerful European Council.
Separately, Mr Rutte refused to rule out the prospect of Ireland's securing a deal to reduce our crippling legacy debt.
He said issues such as legacy debt were not off the table but he warned that there were more immediate matters that must be dealt with by European Union leaders.