Kenny still in contention for European position despite denials
However, ministers are playing down the prospect of Mr Kenny departing to Brussels.
Mr Kenny's name is being linked with the role of European Council President, which comes up in the autumn.
Crucially, the Taoiseach has a strong relationship with German Chancellor Angela Merkel, who is also in Dublin for the EPP Congress. Mr Kenny will again push for the promise of a legacy bank debt deal to be fulfilled when he holds talks with Ms Merkel today.
The Taoiseach is technically out of the running to be the EPP's nominee for the European Commission Presidency.
The pair are going up against each other in a run-off election to be held at the EPP Congress today, with the winner becoming known by lunchtime.
As a major block in the EU, an EPP figure is likely to either become European Commission President or European Council President.
Mr Kenny's name continues to be associated with the latter position.
Former European Affairs Minister Lucinda Creighton said the Taoiseach would be a strong candidate for the Council presidency.
"There is a very positive perception of Ireland in European circles, and I think he certainly would be a name that would be in contention," she said. "It would be a great honour, and one that I think he would have to consider very, very carefully."
Junior finance minister Brian Hayes dismissed the speculation surrounding the Taoiseach. "I think his focus is on the election in 2016 and trying to return the current Government," he said.
European Affairs Minister Paschal Donohoe said Mr Kenny will pass up the chance to take up a top post in Europe.
Speaking at the National Convention Centre, Mr Donohoe said he believed Mr Kenny was staying put.
"My view is that he is staying. I genuinely believe that he is absolutely committed to ensuring this Government continues with its work to support and complete our recovery," he said.
When asked if he would reconsider going for the European job, Mr Kenny said: "What would I do without Mick Wallace and Boyd-Barrett and all the people there. I have to have a bit of life at times."