An Irish government spokesman said the trip had been "postponed for scheduling reasons".
He said the way Mr Trump's visit and expected cancellation played out had been "extraordinary", adding the Government "hadn't been alerted that the visit was on in the first instance".
But White House spokeswoman Sarah Sanders told reporters that no final decision had been made.
It is understood officials in Dublin are awaiting word on whether the review will impact on the Irish leg of President Trump's itinerary.
"The president will travel to Paris in November as previously announced", she said.
"It came a little bit out of the blue", said Irish Prime Minister Leo Varadkar on Sept 2.
"We were taken by surprise when the news broke that he was not coming, as we were when it was announced he was coming", the source said.
There were plans for Trump to spend one day in the capital before travelling to Doonbeg in County Clare where he owns a golf course.
The extend within the president's search the advice of with might presumably presumably also just come as a relief, with several Irish political parties suggesting they'd stage protests which can presumably maybe contemporary a diplomatic predicament for the government.
Brendan Howlin, the leader of the Irish Labour Party, accused Trump of being "no friend of democracy and human rights" in an August 31 tweet calling on people to join anti-Trump protests.
In its announcement, the White House said the visit would serve to "renew the deep and historic ties between our two nations".
Trump's family business operates a golf club on Ireland's west coast.
The President's trip, planned for November 12th after Armistice Day commemorations in France, will not now happen.