Mr Varadkar told her that the European Union would never accept an arrangement that allowed Britain unilaterally to pull the plug on the "backstop".
"Looks like we're heading for no deal", Jeffrey Donaldson, one of 10 Democratic Unionist Party (DUP) lawmakers whose support May now needs to get any deal passed in the British parliament, said on Twitter.
With just five months until Britain is due to leave the EU, May has yet to nail down a divorce deal, with the insurance arrangement to keep open the border between British-ruled Northern Ireland and EU member state Ireland still the outstanding issue.
Mr Raab's proposal to Mr Coveney was that within three months of the backstop coming into force - or six months at the very most - Britain would have the right to trigger a "review mechanism" in which the backstop would persist only by "mutual consent".
But Britain's Conservative government and its Northern Irish ally, the Democratic Unionist Party, will not accept that because it would mean customs and regulatory checks between Northern Ireland and the rest of the UK.
British Prime Minister Theresa May's office has dismissed as "speculation" a newspaper report that suggests an all-UK customs deal will be written into the legally binding agreement governing Britain's withdrawal from the EU.
The EU agreed to a compromise on the backstop agreement to keep the border between Northern Ireland and Ireland last week, signalling they would accept keeping the whole of the United Kingdom in a customs union until both sides sign up to a deal that would prevent the need for a hard border.
However, Leo Varadkar, the Irish prime minister, said that Dublin was open to the idea of a "review mechanism" for the backstop that had been put forward by Mrs May in a telephone call.
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But sometimes patience is short and frustration is there. I think we're so close to getting the last level. I think I'm at a great place to do that".
"We are making good progress on the future relationship, and 95% of the Withdrawal Agreement has been settled.
He recalled the prior commitments made that the backstop must apply "unless and until" alternative arrangements are agreed". Alternatively, it is proposed to establish in Northern Ireland a free customs zone, which, in turn, resent the EU.
Grieve rejected the argument that MPs should back whatever deal Theresa May secures in order to avoid a disorderly exit from the European Union, repeating his call for any deal to be put to a second referendum.
"Looks like we're heading for no deal", he tweeted.
"I am extremely confident we will reach an imminent deal", Glen told a financial services conference in London.
Even if a deal is done in Brussels in the coming days, May will have to sell it in London - first to her own Cabinet, and then to Parliament.