Mr Varadkar also rejected proposals now being examined which would mean anyone crossing the border would have to pre-register in order to avoid checks.
Vardakar urged senior cabinet figures to visit the border for a better understanding.
Speaking from the USA, where he is conducting a series of St Patrick's Day engagements, Varadkar said: "No, it is not a solution that we envisage".
Mr Hastings, who is Vice Chair of the North West Cross Border Group, said it was clear that the British Government had no idea of the real depth of the border challenge and how many areas of cooperation Brexit threatened to sever.
He said Northern Secretary Karen Bradley had already done so, as have a number of MPs and members of the House of Lords.
"As is always the case and this is true for any politicians or anyone in any walk of life you can read as many briefing documents as you like sometimes you need to see things with your own eyes, and I think for that reason, they would be very welcome to visit the border and see it for themselves".
Due to the sluggish process of exit negotiations, German companies increasingly expect a "hard" Brexit in which Britain leaves the single market and loses most of its now privileged access to the European Union internal market. Our preferred option is a deep and comprehensive agreement between the European Union and the United Kingdom in its entirety which will allow us to trade as we do now.
Talks regarding the Irish border remain a critical issue in Brexit negotiations, where there is now no clear plan on how to avoid the customs and sanitary checks. Hain said that the proposal of pre-registering "would be risking immediate civil unrest".
Last week Mr Varadkar rejected a suggestion by British Prime Minister Theresa May that the customs arrangement between the United States and Canada was among possible models for the future arrangement in Ireland.
The British government wants to leave the customs union and has rejected a so-called "backstop" option put forward by the EU which would see Northern Ireland remain in the customs union if a comprehensive deal can't be agreed with the UK.
If border posts return to Northern Ireland they will be attacked, according to the Taoiseach.
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