The Prime Minister, who was using the G7 summit in Biarritz to hold talks with European Council president Donald Tusk on Sunday, said he believed the chances of a deal were "improving" following a round of diplomacy which has also seen meetings with Germany's Angela Merkel and France's Emmanuel Macron.
But he refused to repeat his previous assertion that the odds of a no-deal outcome were a million to one.
He told the BBC: "It all depends on our EU friends and partners. I think in the last few days there has been a dawning realisation in Brussels and other European capital what the shape of the problem is for the UK.
"I think it's going to be touch and go but the important thing is to get ready to come out without a deal."
In a series of broadcast interviews on Sunday, Mr Johnson confirmed he would withhold the bulk of the £39 billion Brexit divorce bill if there is not a deal.
He told Sky: "I think what the entire European Union understands is that if we come out without a deal that the £39 billion is not pledged.
If there was a no-deal Brexit, he said he would "guarantee" that people would still be able to get medicine and "I think it's highly unlikely that there will be food shortages of any kind". This had been speculated in the leaked "Operation Yellowhammer" dossier, for which Mr Johnson came under fire from Philip Hammond on Sunday morning.
Mr Johnson went for a swim in the Atlantic before his meetings at the G7 and told ITV: "I swam round that rock this morning. From here you cannot tell there is a gigantic hole in that rock. There is a way through.
"My point to the EU is that there is a way through, but you can't find the way through if you just sit on the beach."
Before the summit, Mr Tusk urged Mr Johnson not to go down in history as "Mr no-deal".
The Prime Minister told Sky: "The people who are going to be responsible for no deal are not in the UK, we don't want no-deal."
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His comments came as he faced a backlash over reports he had sought legal advice from attorney general Geoffrey Cox about temporarily shutting down Parliament - known as prorogation - for five weeks from September 9.
The Observer reported that the move would allow for a Queen's Speech, starting a new parliamentary session, on October 14.
Such a move would keep MPs away from the Commons until shortly before the European Council summit of EU leaders on October 17, potentially preventing moves to block a no-deal Brexit.