"We face enormous challenges from Brexit, which has undoubtedly changed the political climate in Northern Ireland", Varadkar said in the text of a speech due to be delivered at an event in Washington celebrating 20 years of peach in Northern Ireland.
Former taoiseach Enda Kenny invited Mr Trump to Ireland in the White House when he made the annual St Patrick's Day trip this time past year.
At the time Mr Varadkar - who was the Social Protection Minister - spoke out against inviting Mr Trump to the state saying he "wasn't keen" on the idea.
He also used his address in Washington DC to call for official recognition of the Irish language in Northern Ireland, and said it is damaging for the North to continue without a power-sharing executive.
The Taoiseach's visit to the USA takes a turn today to focus on commerce, with a number of events planned. He has invited me to his house and I think it is just normal hospitality that when someone invites you to their house and their country that you reciprocate the invitation.
The US president owns the Trump International Golf Links and Hotel in Doonbeg in Co Clare.
Mr Pence has often been criticised for his opposition to LGBT rights and his alleged support of conversion therapy.
"The period after Easter should see a redoubled effort on the part of both governments and all of the parties in Northern Ireland to seek agreement on the restorations of the institutions", the Taoiseach said.
"But I imagine if I have the opportunity - I'm going to meet him over breakfast - so if I have the opportunity I'll certainly be mentioning the wider issue of equal rights and freedoms for LGBT".