Tánaiste Simon Coveney has said the EU may offer the UK a 21-month Brexit extension.
Mr Coveney said a long extension to Article 50 would give the UK a "long reflection period" to consider the kind of Brexit it wanted and could facilitate a fundamental rethink.
He told RTÉ's Sean O'Rourke programme that British prime minister Theresa May was offering a "stark choice" to the UK parliament.
"Back a deal by the middle of next week and we'll have a short extension which will essentially be a technical extension to get all the legals in place, or we're essentially looking for, we will look for, a much longer extension to allow Britain to rethink its approach to Brexit," he said.
Mr Coveney said a long extension was "likely to happen" if there was no agreement in the UK Parliament on a deal.
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"If you have a long extension of say 21 months, to the end of 2020, or whatever the period would be, well then Britain has a legal entitlement to have representation in the European Parliament," he said.
Mr Coveney added that the Republic would "continue to prepare" for a no-deal scenario despite the outcome of last night's vote in the House of Commons.
But he said he hoped that over the next week, Brexit would "take a turn in a positive direction" that would provide more certainty.
The tánaiste said the Republic would not present an obstacle to an extension but some European leaders might need convincing.
"Some of the European prime ministers will be quite demanding I think. They are open to an extension of time but they want to know in what detail by providing that extension of time how they get certainty," he said.
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Discussing the UK's proposed tariffs on exports from the Republic in the event of a no-deal, Mr Coveney said: "If they are designed to try to put pressure on Ireland, it's had the opposite effect actually. It's actually galvanised the European Union."
Mr Coveney said he spoke with the EU Commission minutes after the details of the tariffs were published and that he had received a courtesy phone call from his British counterpart informing him of the proposed tariffs before they were announced.
"I don't think it's workable and even the British government themselves say this is a very short-term arrangement," he said.
"What is needed in a no-deal scenario are urgent talks between the Irish government, the British government and the European Commission to put something more viable and sustainable in place."
