The representative of the government of Ireland said that the visit trump was "delayed schedule", according to the Chronicle.info with reference on the European truth.
The White House announced in August that Mr Trump would travel to Ireland as part of a trip to attend the 100th anniversary of the armistice that ended World War One in Paris on 11 November.
On Tuesday, White House press secretary Sarah Huckabee Sanders said that the president would travel to Paris as previously announced.
His office later said it was still possible Mr Trump will take up Mr Varadkar's invitation at a future date, but confirmed November's trip will not be happening.
He had originally been invited by former taoiseach Enda Kelly on his final St. Patrick's Day visit to the White House a year ago, an offer that was reiterated by Mr Varadkar last March.
"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.
The president had planned to visit Dublin and his property in Ireland, a golf resort in Doonberg, on November 10-11 before visiting Paris on November 11.
Officials from the US State Department met with their Irish counterparts at Government Buildings today to discuss the change of plans.
Politicians and activists in Ireland had indicated they would hold protests during Mr Trump's visit.
Irish activists espousing left-wing and environmentalist causes had pledged to hold protests.
The UK campaigners behind the controversial balloon said the Irish trip was an "excellent opportunity" to "troll" Mr Trump yet again.
There has been no official announcement as yet from the White House and no indication that the visit will be rescheduled.
Labour Party leader Brendan Howlin tweeted that Trump "has been no friend of democracy or human rights".
The decision to welcome Mr Trump to Ireland was met with widespread criticism across the political spectrum.
He had been due in Ireland the following day.
That summit, in Helsinki, led to widespread criticism that Trump was deferential to Putin and did not challenge him about Russian interference in the 2016 US presidential election.