The Government has not received any official confirmation that US President Donald Trump will be visiting Ireland next month, a spokesperson has said.
There is growing speculation that a presidential visit will take place in early June but a White House spokesperson told RTÉ News that it had nothing to announce at this moment about such a visit.
Speaking in Paris the Taoiseach said he could not confirm a visit to Ireland by President Trump as protocol normally dictates that the White House makes such announcements "rather than the Irish government."
Leo Varadkar said: "if President Trump comes to Ireland he will be treated with respect and given the welcome his office deserves.
"The President of America is always welcome in Ireland, just as the Taoiseach and Irish President are welcome in the United States. We've a really strong relationship, it's economic, it's cultural, it's historic. It's about our family connections as well.
"I think we have to rise above whoever holds the office, whether it's the office of President there or here or Taoiseach and remember the really important relationship that exists between Ireland and America. That has to be the priority."
Mr Trump will be in Europe next month for a state visit to the UK between 3 and 5 June and a D-Day commemoration in France on 6 June.
During his St Patrick’s Day meeting with the Taoiseach at the White House in March, the US President said he planned to visit Ireland this year.
Leo Varadkar later said that the visit may happen in June when Mr Trump travels to Europe.
Opposition politicians have said that Mr Trump would not be welcome to visit Ireland.
Solidarity-People Before Profit TD Richard Boyd Barrett said Mr Trump's agenda on every imaginable issue represents "a dangerous threat to the world we live in".
Labour Senator Aodhán Ó Ríordáin said the US President is not welcome, adding that the State should not be facilitating a visit that he will seek to exploit for his re-election campaign.
The co-leaders of the Social Democrats, Róisín Shortall and Catherine Murphy, also issued a statement saying they are "strongly opposed" to any such visit.