Boris Johnson will tell EU leaders there needs to be a new Brexit deal when he makes his first trip abroad as PM later this week.
The UK will leave the EU on 31 October with or without a deal, he will insist.
However No 10 said there will “very little discussion” of Brexit during the meetings in France and Germany.
Meanwhile, the Sunday Times has printed leaked government documents warning of food, medicine and fuel shortages in a no-deal scenario.
It says the Treasury paper on preparations for a no-deal Brexit, codenamed Operation Yellowhammer, reveals that the UK could also face months of disruption at its ports, while plans to avoid a hard border between Northern Ireland and the Republic of Ireland are unlikely to prove sustainable.
The government said the document was not what the government expected to happen, but scenarios being looked at as part of no-deal preparation.
The prime minister will travel to Berlin to meet German Chancellor Angela Merkel on Wednesday, and meet French President Emmanuel Macron in Paris on Thursday.
He is expected to say that parliament cannot and will not change the outcome of the 2016 referendum and insist there must be a new deal to replace Theresa May’s Withdrawal Agreement – which was defeated three times – if the UK is to leave the EU with a deal.
However, it is thought that the leaders are more likely to discuss issues other than Brexit, such as foreign policy, security, trade and the environment, ahead of the G7 summit next weekend.
Boris Johnson had been reluctant to fly to meet European leaders until it seemed a breakthrough was likely.
But – it still doesn’t.
When Mr Johnson meets the EU’s most powerful leaders – Angela Merkel and Emmanuel Macron – he will repeat his message that the UK is leaving, no matter what, at the end of October.
He will tell them face-to-face for the first time that the only way the UK will sign up to a deal is if the EU thinks again, and replaces the agreement brokered by Theresa May.
But there seems to be little chance of any serious progress in the coming days.
No 10 does not seem particularly optimistic and says that it expects both sides will say their piece, then move on to other issues.
Meanwhile Labour leader Jeremy Corbyn has reiterated his call for MPs to work together to stop no-deal Brexit.
Speaking to the Observer, Mr Corbyn said his plan to be installed as a caretaker PM – so he could delay Brexit, call a snap election, and campaign for another referendum – was the “simplest and most democratic way to stop no-deal”.
“We have to seize the opportunity before it’s too late, so the people, rather than an unelected prime minister, can decide our country’s future,” he said.
Several Tory MPs and Liberal Democrats rejected his proposals, although it won the the potential backing of the SNP and Plaid Cymru.
Lib Dem leader Jo Swinson said Mr Corbyn was “divisive” and instead suggested that Conservative MP Ken Clarke or former Labour leader Harriet Harman could head a temporary government.
Meanwhile, in a letter seen by the Mail on Sunday, Mr Johnson has warned rebel Tory MPs that their opposition to a no-deal Brexit is damaging the prospect of getting a new deal.
He said it was “plain as a pikestaff” that the EU will “not compromise as long as they believe there is the faintest possibility that Parliament can block Brexit on 31 October”.
More than 100 MPs from across the Commons have urged the prime minister to recall parliament and let it sit permanently until the UK leaves the EU.
In a letter, MPs say: “Our country is on the brink of an economic crisis, as we career towards a no-deal Brexit which will have an immediate effect on food and medical supplies, damage our economy, jobs, the public finances, public services, universities and long-term economic security.
“We face a national emergency, and parliament must be recalled now in August and sit permanently until 31 October, so that the voices of the people can be heard, and that there can be proper scrutiny of your government.”