The Prime Minister told French president Emmanuel Macron that Brussels "must match the compromises that the United Kingdom has made in recent weeks and months" if a no-deal Brexit is to be avoided.
He said: "John Major has explained that Johnson might be able to bypass the anti-No Deal legislation by "passing an Order of Council to suspend the Act until after 31 October".
Barnier told an event in France Saturday that while an agreement was still possible it "will be very hard to reach".
The only question is whether Brussels (the EU) will happily fire us with a mutual agreement, or force us to leave at our own risk, said the conservative ruler in two public articles in two Sunday newspapers.
"In the detail of the negotiations, of course we can get into the detail as to how operationally they work, what legal certainty is required", he said.
The EU refuses to characterise the talks held so far as negotiations, preferring to resurrect a Brexit withdrawal agreement struck with Johnson's predecessor Theresa May that has been rejected three times by British MPs.
"We will be packing our bags and walking out on" October 31, Boris Johnson wrote in The Sun on Sunday and Sunday Express newspapers. In essence, Johnson proposes that the British province of Northern Ireland leave the European customs union together with the rest of the United Kingdom once Brexit is consummated, but continue within the single market until 2025, when it would be up to the Norwegian Assembly to decide whether to continue under that regime, or abide by British rules.
Writing in two other Sunday newspapers "The Sun on Sunday" and "Sunday Express" Johnson himself reiterated his stance against the controversial Irish backstop and said his untested plan to use technology to eliminate customs border checks would take the United Kingdom out of European Union trade rules while respecting the Northern Ireland peace process.
This border plan is not acceptable for the EU.
But the EU's chief Brexit negotiator Michel Barnier poured scorn on the chances of the new proposal succeeding, reportedly telling an event in Paris: "If they do not change, I do not believe, on the basis of the mandate I have been given by the EU27, that we can advance". "On October 31 we are going to get Brexit done".
Ireland's leader Leo Varadkar said Saturday there is "plenty of time" to put forward alternatives and he was trying to arrange a meeting with Johnson next week, Irish broadcaster RTE reported. It sees the potential for rampant smuggling - especially as Johnson intends for the rest of the United Kingdom to diverge from European Union labour, environmental and tax norms to aim for a regulation-lite economy on Europe's doorstep.
But the PM has won the backing of former premier David Cameron, who said he "completely supports" Mr Johnson's efforts to get a deal in Europe and take it through the Commons, adding: "That's the best thing that could possibly happen".
Government papers submitted to a Scottish court said that Mr Johnson will comply, despite his assertion that there will be "no more dither or delay".