A spokeswoman for the Irish government told CNN the United States had postponed the visit citing scheduling reasons on the U.S. side.
He told Irish radio station RTE on September 2: "There is an open invitation to the US President to visit Ireland at any time".
Irish Prime Minister Leo Varadkar's administration was "caught totally unaware" when asked by the Independent - and a spokesman said he could not confirm any new developments.
In addition to visiting the Irish capital of Dublin, Trump was expected to travel to a golf course he bought in County Clare in 2014.
Politicians and activists in Ireland had indicated they would hold protests during Mr Trump's visit. Other protests were planned in Dublin and other Irish cities.
Ireland's opposition Green Party, which had opposed the trip, described the announcement and following cancellation as "erratic".
Mr Coveney said: "It will be controversial because everything Donald Trump does these days is controversial".
However, widespread reports emerging this afternoon suggest that he has cancelled the visit. Scientists say those threats are the effect of something for which Trump has firmly rejected government planning: climate change.
Brendan Howlin, leader of the Labour Party in the Republic, said Mr Trump was "no friend of democracy or human rights".
The decision to welcome Mr Trump to Ireland was met with widespread criticism across the political spectrum.
The brief trip to Ireland was scheduled to take place as he made his way home from Armistice Day commemorations in France on November 11.
The trip to Ireland would be Trump's first to the country as President but his reception there was expected to be frosty.