In a BBC interview at the G7 summit in France, he said it "all depends on our EU friends and partners".
When pressed on the chances, he said: "I think it's going to be touch and go. But the important thing is to get ready to come out without a deal."
European Council President Donald Tusk told Johnson the EU is open to alternatives to the backstop.
Tusk and Johnson held talks on Sunday, which were in a "genuinely positive atmosphere".
Tusk repeated the EU's position that any alternatives to the Irish backstop would have to be "realistic" and "immediately operational".
An EU official added the meeting had "mainly restated known positions" and Brussels had been hoping for "new elements to unblock the situation".
The two men clashed on Saturday over who would be "Mr No Deal" - the person to blame in the case of a no-deal Brexit.
Johnson has previously said the UK must leave on October 31 "deal or no deal", but that the chances of a no-deal Brexit happening are a "million to one".
Asked if people would still be able to get their medicine if there was a no-deal Brexit, the Prime Minister told the BBC: "That is certainly a guarantee that we can make."
But he added: "I do not want at this stage to say there won't be unforeseen difficulties."
Speaking at the G7 summit on Sunday, he reiterated his desire to scrap the backstop from the current withdrawal agreement, saying it could keep the UK "locked in" EU rules, if a trade deal is not agreed after Brexit.
He said: "I think in the last few days there has been a dawning realisation in Brussels and other European capitals what the shape of the problem is for the UK."
Johnson said he was an "optimist" and thought the EU would understand there is an "opportunity to do a deal".
The Prime Minister also said if there is no deal, the UK would keep a "very substantial" part of the 39 billion pounds former PM Theresa May had agreed to pay the EU in her withdrawal agreement.
The G7 summit a get-together of most of the leaders of the world's largest economies comes with just over two months until the UK is scheduled to leave the EU at the end of October.
( With inputs from IANS )