The prime minister put forward revised proposals for a deal last week, created to avoid a hard border on the island of Ireland after Brexit.
Mr Burleigh's initial claim that Barnier has been given the "green light" for such talks now seems uncertain, however, with a number of other reporters inflicting an abundance of mixed metaphors on observers by suggesting that the governments of the EU27 will not enter a "tunnel" with the British without being able to see a "landing zone" at the end of it.
The main stumbling block remains the border between Northern Ireland and Ireland, the United Kingdom's only land border with the EU.
Boris Johnson's government is set to enter intensive "tunnel" negotiations with the European Union over a possible Brexit deal ahead of a crunch summit in Brussels next weekend, in a major boost for the prospect of an agreement before the October 31 deadline.More news: Samsung Could Be Launching Galaxy S11 Lite
"If Boris Johnson does manage to negotiate a deal then we will insist that it is put back to the people in a confirmatory vote", he said. "We need vigilance, determination and patience", said the man who once organized the 1992 Winter Olympics in his region of France. Johnson's Brexit Secretary, Stephen Barclay, got a warm welcome from European Union negotiator Michel Barnier before they started nearly two hours of talks Friday around breakfast.
"If he can't - or I should say won't - get a deal we will take whatever steps are necessary to prevent our country crashing out of the European Union without a deal", he said.
As the negotiators reviewed their options, the president of the European Council and host of next week's Brussels summit Donald Tusk said that he would have pulled the plug on talks this Friday if Britain had not come forward with evidence of a workable proposal.
The prime minister cautioned it was not a "done deal" and there was still "a way to go" if they were to get an agreement which would enable Britain to leave on October 31, as he has promised.More news: Modi-Xi summit: Had ‘heart-to-heart’ talks, says Chinese President Xi Jinping
Just two days before Thursday's breakthrough, Johnson's advisors said that brokering a compromise was "essentially impossible" following a hard meeting with German Chancellor Angela Merkel.
The UK presented alternative plans last week which would see Northern Ireland remains in the customs union for goods and agri-food products with physical checks to be conducted away from the border.
If no deal is obtained next week, the sitting would also mark a crunch decision on whether Johnson agrees to request a three-month extension to the Article 50 process or is forced to resign.
Varadkar's words Thursday indicated that Johnson might have shifted his red lines and could now be willing to keep Northern Ireland in the customs union.More news: Season 23 of 'South Park' fights against Chinese censors