It comes as the sixth round of negotiations come to a close in Brussels with British and European Union negotiators are due to hold a press conference.
After another inconclusive negotiating session, both sides said differences remained on vital divorce issues including Britain's Brexit bill, the Irish border and the rights of citizens affected by Brexit.
"This should lead us to identify the technical and regulatory solutions necessary to prevent a hard border while preserving the integrity of the single market".
The working paper, seen by RTÉ News, said that in order to avoid a hard border it is essential that there be no divergence of rules on either side of the Irish border.
On citizens' rights Barnier commended the UK's plans on registering European Union citizens after Brexit, and said it was a "useful clarification, and good basis for further work".
It was circulated to the 27 member states on Wednesday night and presented to British negotiators in Brussels yesterday.
The government has been reassured by indications that some Eurosceptics are prepared to pay a little more as the price for ensuring Britain heads out of the exit door.
Although there would need to be "specific solutions" for the unique position of Northern Ireland "this can not amount to creating a new border inside our United Kingdom".
Now, there are most likely three broad possible outcomes of the negotiations.
"Only sufficient progress - that is to say honest and real progress - on the three main key issues of these negotiations will enable the triggering of the second phase of our negotiation", he said.
The UK was "ready and willing" to engage with Brussels "as often and as quickly as needed" ahead of the 14-15 December summit, he said.
"The fact is that a political decision has been made, in this country, to maintain that there can be no going back", he will say. This remains Ireland's best option.
The Taoiseach said there had been agreement that there would no return to the border of the past.
He said: "While we're in, we're in".
Kerr said the British government has misled voters into believing the process is unstoppable.
Britain has tried to nuance this, saying that there are ways to lessen the impact of an Irish Border and that in any case this can not be finally sorted until it becomes clear what the future trading arrangement would be between the United Kingdom and the EU.
Mr Brokenshire said he found it "difficult to imagine how Northern Ireland could somehow remain "in" while the rest of the country leaves".
He said Fine Gael is holding its party conference in the border area of Cavan this weekend, as it is very concerned about what the future holds in the border area in the context of Brexit.
The Democratic Unionist Party (DUP) meanwhile has repeatedly warned that it will not accept any deal that undermines the union between Britain and Northern Ireland.
European Union leaders are due to assess at a December 14-15 summit whether "sufficient progress" has been made on divorce terms to move to phase two of the talks, as Britain desires.
Barnier said "some progress" had been made but he wanted reassurances on the divorce bill before he would greenlight discussions on the future relationship between the United Kingdom and the bloc. The EU is suggesting to London that the current Border fudge is not enough.