With just five months until Britain is due to exit the EU, May has yet to nail down a divorce deal, with the Irish border insurance arrangement to keep open the border between British-ruled Northern Ireland and EU member state Ireland still the oustanding issue.
The opposition Labour Party has all but ruled out supporting any deal May reaches with Brussels, leaving the prime minister reliant on her slender parliamentary majority that comprises her own divided MPs and coalition partners the Democratic Unionist party.
"These ideas are not backstops at all and don't deliver the UK's obligations", the spokesman said.
The key sticking point in talks remains how to avoid customs checks at the post-Brexit border between Northern Ireland and the Irish Republic without putting up new barriers between Northern Ireland and the British mainland.
Coveney made his comment after Britain's Daily Telegraph reported that Prime Minister Theresa May's Brexit Minister Dominic Raab had privately demanded the right to pull Britain out of the backstop after three months.
Taoiseach and Fine Gael leader Leo Varadkar with Minister for Foreign Affairs Simon Coveney speaking to the media at Stormont House about Northern Ireland and Brexit earlier this year.
The Democratic Unionist Party (DUP), whose 10 MPs prop up Theresa May's government, warned on Tuesday that the United Kingdom is heading for a no-deal Brexit, even after Irish prime minister Leo Varadkar on Monday signalled a willingness to consider a review process for the Northern Ireland backstop.
A Downing Street spokesman said on Sunday the report was "speculation" and that negotiations with the European Union are ongoing, although he reiterated the government's line that the withdrawal agreement is 95 per cent complete and that it's making progress on the future relationship.
British Prime Minister Theresa May will bring plans to avoid a hard Border to her divided cabinet tomorrow. "In terms of resolving those, those talks are ongoing", the spokesman said. But that goal has been complicated by May's intention to take Britain out of the EU customs union and single market. Brussels rejected her plan to let mainland Britain, too, enjoy special access to the European Union market - but the two sides have since come closer on a possible plan.
But there are significant worries that any deal or end to the backstop that would result in a hard border could threaten the peace process.
"While we too hope the Northern Ireland backstop will never be required to be used, it will be required to be written down in legal text".
But the government's Brexit department stated that they are confident there will be a deal that works for businesses - and reiterated their stance against a People's Vote.