Coveney had noted that Ireland's position on the Northern Ireland backstop "remains consistent", and that a time-limited backstop "that could be ended by United Kingdom unilaterally would never be agreed".
But this has been rejected by London, as it would see customs checks take place between Northern Ireland and the rest of the UK.
"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".
May is under intense pressure from several members of her cabinet to secure a mechanism by which any backstop agreements can be time limited and able to be terminated by the UK.
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".
At the same time, it reported there would be an "exit clause" in the deal to convince Brexiteers in Parliament that the arrangement - which they oppose - would not be permanent.
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"We have made good progress but clearly in relation to the backstop there are outstanding and significant issues".
The backstop ensures that Northern Ireland would stay "aligned" to the regulations of the single market and the customs union if there is still no other solution that would avoid infrastructure along the Irish border.
Rumours are swirling about how close, or not, we are to a Brexit deal.
Speaking at a meeting of the British-Irish Intergovernmental Conference in Dublin, Mr Coveney said he believed "it is possible to get a deal in November", adding: "This border issue is complicated to resolve. but I think we're very close to resolving it".
He argued that Britain would effectively become a non-voting member of the European Union, having to accept laws made in Brussels with no power to influence them.
"He recalled the prior commitments made that the backstop must apply "unless and until" alternative arrangements are agreed".
Labour peer Baroness Kennedy QC, former Court of Appeal judge Konrad Schiemann and David Edward, a former judge of the Court of Justice of the European Communities are among those who have called for a People's Vote on EU membership.
"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.