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Brexit and the political stalemate at Stormont are expected to be discussed when he meets with the political leaders.
The future of relationships in the Republic and Northern Ireland, post Brexit will also be the focus of a keynote address the Taoiseach will deliver at Queen's University in Belfast.
Relations between the Irish Government and the DUP, Northern Ireland's biggest party, remain strained after Mr Varadkar said Ireland would not help Britain design an economic border for Brexiteers.
He said Brexiteers were the ones who wanted a border so it is up to them to design one.
The DUP's Arlene Foster described the comments as "not helpful" and said she was looking forward to meeting with the Taoiseach to discuss a number of issues.
The SDLP said yesterday that it intends to ensure Mr Varadkar will not sway from his position that there can be no new economic or physical border imposed on the island of Ireland.
Party leader Colum Eastwood also said he will be asking the Taoiseach to become more directly involved in the crisis talks at Stormont aimed at restoring power-sharing.
Sinn Fein's Gerry Adams said his party will be telling Mr Varadkar that the Irish government has a responsibility to defend the Remain vote.
Mr Adams said the Taoiseach has to challenge any proposals that would see an economic border on the island of Ireland.
The issue of same-sex marriage may also be discussed as Mr Varadkar intends to participate in a gay Pride breakfast event in Belfast on Saturday to promote the rights of the LGBT community.