Mr Varadkar is the Republic of Ireland's first openly gay taoiseach and will attend a pride festival breakfast event on Saturday morning.
"This is the space in which agreements are made", he said.
Theresa May's decision to leave the single market and customs union has also led to growing uncertainty in Northern Ireland.
In a marked shift of tone from Dublin Leo Varadkar used his first visit to Northern Ireland as taoiseach to demand that London drop its plans for a so-called technological solution to the Irish border.
"But we think putting forward our view that remaining in the customs union would resolve many of these issues on the border of the isle of Ireland, that seems to us to be a practical solution".
Mulhall described the figure as "an extraordinary number", and said he thought it was a sign that people were seeking "to safeguard their position for the future". But if it is to be free for trade as well as people, and if businesses and citizens are to avoid disruption, the United Kingdom must remain a member of the single market and the Customs Union.
The taoiseach referred to the lack of input into the Brexit debate from Northern Ireland due to the collapse of the Stormont executive.
"We have to negotiate our way through this".
He said that throughout political history, there was a precedence of people changing their minds.
After holding a meeting with the Taoiseach in Belfast later on Friday, Mrs Foster said the options for Brexit were "not binary", dismissing the characterisation of hard and soft exits. He also flagged the possibility of a transition period during which the the United Kingdom remains in the single market and customs union. We have a vital interest in a Britain that is outward-looking, prosperous and on good terms with its neighbours.
"There is no practical hard-border solution available, therefore, you have to find what the European Union negotiating directive calls imaginative and flexible solutions". Mr Varadkar said it was not clear if that would happen before a summit in October. They've already had 14 months to do so.
Even though some of the North American models are tested and true, she wants to see Northern Ireland make improvements, particularly when it comes to wait times for visa applications. However, the Scottish government remains committed to holding another referendum.
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