The talks come with time running out to sign off on any agreement at a 17-18 October leaders' summit in Brussels, ahead of the UK's scheduled departure from the European Union at the end of the month after almost five decades of membership.
Johnson has vowed Britain will leave on October 31 with or without a deal - despite MPs passing a law last month that requires him to seek another Brexit delay if he fails to secure a pact at the summit.
"As far as the Irish government is concerned, we do want a deal, we're willing to work hard to get a deal, to work until the last moment to get a deal, but certainly not at any cost".
Talks with the European Union to reach an agreement on Britain's departure have hit an impasse over the backstop, an insurance policy to prevent the return to a hard border between the British province of Northern Ireland and European Union member Ireland if a future trade deal falls short of keeping the border open.
"Brexit will remain the defining political issue of our time, with the prospect of a decade or more of bad-tempered negotiations, internal political rows, and uncertainty for business and citizens", MacShane said.
"That's why I think it is better now to focus on what we can do in terms of concluding that deal, something which is desirable and still, in my view, possible".
European officials warned Monday (6 October) that Britain's latest Brexit proposal can not serve as a basis for a breakthrough before next week's Brussels summit.
Pound Sterling remains under pressure against the Euro, Dollar and other major currencies with foreign exchange markets widely expected to take their next cues on the currency from a meeting of the leaders of the United Kingdom and Ireland.
"The EU will stay calm, attentive, respectful and constructive", Barnier said.
In the fevered atmosphere surrounding Brexit where newspaper reports and contradictory tweets can send sterling into gyrations, European Union officials denied a report in The Times that the bloc was preparing a major concession to Britain to secure a deal.
Mr Johnson will hope to see concessions on the issue of the Irish backstop, the contingency measure to prevent a hard border on the island which has proved a persistent sticking point.
The PM has talked about that whereas he'll abide by the regulation, he is set up to leave on the Halloween lower-off date attain what could well moreover.
"I had a very good meeting with the prime minister... very positive and very promising", Varadkar said. "At best No Deal Brexit risks have only been pushed out rather than diminished", says Derek Halpenny, a foreign exchange analyst with MUFG in London.
"We are not accepting this blame game which started in London", he said.
The British chief's plans would additionally see Northern Irish politicians given a vote each 4 years on sustaining the agreed preparations.