The Dáil has been told that if Article 50 is extended into the summer, then the UK may have to hold elections to the European parliament, and Ireland will be temporarily unable to take up its extra two seats.
The Taoiseach told the Dáil that in this event, the last person elected in the constituencies of Dublin and Ireland South will not take up their seat in the European Parliament until the UK has left.
Ireland gained an additional two MEPs when the European Council redistributed 27 of the UK’s seats for the next parliament, bringing the number of Irish MEPs to 13.
Mr Varadkar also told the Dáil that should the UK leave before the European elections take place, UK citizens resident in Ireland will not be able to vote in the European elections as they won't be EU citizens.
He said this was "unfortunate" but they could find no way around it as it would require an amendment to the relevant treaties.
He added that UK citizens in Ireland will continue to be able to vote in local, Dáil and Seanad elections.
Mr Varadkar also said they had seen no proposals from the UK regarding "alternative arrangements", adding that he had raised the possibility of an extension of Article 50 with Mrs May.
"The Prime Minister has made her position clear, that she intends that the United Kingdom will leave the European Union on time, on the date that they have set for it," Mr Varadkar said.
He also said he did not envisage a different Withdrawal Agreement to the one on the table emerging, "even if that involves a period of uncertainty after 29 March".
Mr Varadkar added that he had yet to see any "alternative arrangements" from the UK.
He also rejected the proposal of a backstop with a time limit: "As the PM eloquently explained herself when she was advocating for the backstop - an insurance policy that can be cancelled at the time when you most need it, is not an insurance policy at all."
