It came after Mr Trump signed executive orders aimed at cracking down on illegal immigrants, including the recruitment of 10,000 new immigration and enforcement officers to carry out deportations.
In a wide-ranging interview with reporters, Mr Kenny said he trusted that Mr Trump would provide a clarification around this which would exempt the undocumented Irish.
“I listened to the president yesterday saying that he has a big heart and if I follow on from what he said before, I trust that in his clarification here that Irish will not be affected by that. It’s an issue I have raised with him and I will raise with him again when I go to the White House,” he said.
Mr Kenny is due to travel to Washington, DC, for St Patrick’s Day.
Mr Kenny’s comments were in stark contrast to what he said before Mr Trump’s election when he accused him of using “racist and dangerous” language.
Mr Trump has signed off on building a wall between the US and Mexico and has also approved a raft of other orders aimed at tackling illegal immigration since he entered office.
The measures would make it easier for undocumented immigrants to be classed as criminals and therefore made a priority for deportation.
Mr Kenny said those from Ireland who are living illegally in the US “contribute very strongly to the American economy” and he hoped this would be acknowledged.
He said there were now questions around whether a person could be deported because of a parking ticket they received 10 years ago.
“I do hope that given the extraordinary contribution people make in terms of social security employment opportunities, contributing to American society, that the clarification is about serious indiscretions.”
Asked about the decision to start building the wall, Mr Kenny said: “Sure there was a fence there for about a third of it already. Obviously the president has signed his executive order, as he said he would.”
Mr Kenny also indicated he would be remaining on as leader of Fine Gael until 2018.