Speaking for the first time since a crunch meeting in Brussels, the PM said "now is the time" for firms and people to prepare for a no deal outcome.
Talks continue between the two sides, but Mr Johnson said they were "not yet there at all" in securing a deal.
Time is running out to reach an agreement before the UK stops following EU trade rules on 31 December.
Weeks of intensive talks between officials have failed to overcome obstacles in key areas, including competition rules and fishing rights.
Mr Johnson met European Commission President Ursula von der Leyen on Wednesday, but the pair failed to make a breakthrough.
Mr Johnson said British negotiators were going to "go the extra mile", and he was prepared to travel to Paris or Berlin for talks if necessary.
But he said the EU wanted to keep the UK "locked" into its legal system, or face punishments such as taxes on imports, which had "made things much more difficult".
The PM added that the EU's proposals would mean, despite leaving the bloc earlier this year, the UK would be forced to remain a "twin" of the 27-country organisation.
"At the moment, I have to tell you in all candour, the treaty is not there yet and that was the strong view of our cabinet," he said.
The two sides have said there will be a final decision on a whether a trade deal can be done on Sunday.
The UK is understood to have offered fresh proposals on Wednesday night but that did not lead to a breakthrough and a senior Downing street source indicated talks could continue beyond Sunday if progress had been made.
Brexit - The basics
- Brexit happened but rules didn't change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards - they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
But Mr Johnson said that "looking at where we are," it was vital the UK prepares for the "Australian-style option" of not having a free trade deal with the EU.
"There's a strong possibility that we will have a solution much more like Australian relationship with the EU than a Canadian relationship with the EU," he added.
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