He was expected to visit his golf course in Doonbeg, Co Clare, and Dublin around the weekend of 10-11 November.
An advance party from the White House was due to visit Ireland in the coming weeks to plan the trip but RTÉ News understands, from sources on both the Irish and US side, that it has now been cancelled.
The White House announced on 31 August that Mr Trump will travel to Paris in November to participate in a commemoration of the 100th anniversary of the Armistice that ended the fighting in World War I. His visit to Ireland was due to coincide with that trip.
Following the confirmation of Mr Trump’s visit there were calls for protests. The Labour Party, Green Party and Solidarity-People Before Profit pledged to organise protests surrounding the visit.
Mr Varadkar said there is a standing invitation for any US president to come to Ireland and many have in the past.
It is believed that no formal communication has been made to the Irish Government yet.