The UK is not prepared to postpone Brexit beyond the current 31 October deadline, Boris Johnson is to tell European Commission President Jean-Claude Juncker at talks on Monday.
The lunchtime meeting in Luxembourg will be the first time the pair have met since the PM took office in July.
A Downing Street source says Mr Johnson will stress he wants to secure a deal by 18 October, after a key EU summit.
But if not possible he will "reject any delay offered" and leave with no deal.
The source said Mr Johnson "would make clear that he would not countenance any more delays".
They added: "Any further extension would be a huge mistake. It is not just a question of the extra dither and delay - it is also the additional long months of rancour and division, and all at huge expense."
The EU's chief Brexit negotiator Michel Barnier will also attend the meeting in Luxembourg, while Mr Johnson will be accompanied by Brexit Secretary Steve Barclay and Downing Street's Brexit representative David Frost, reports the BBC.
Interviewed on Sky News on Sunday, Mr Barclay said a "landing zone" for an agreement was in sight and a "huge amount has been happening behind the scenes". And Home Secretary Priti Patel said the "entire machinery of government" was focused on getting a deal.
The prime minister has also said he is "cautiously optimistic" a Brexit deal can be reached, although Mr Barnier said last week there were no "reasons to be optimistic".
MPs have passed a law that would force the prime minister to ask the EU for an extension to the 31 October deadline if a deal was not agreed by 19 October.
Writing in Monday's Daily Telegraph, Mr Johnson said a large number of MPs were "simply trying to crush Brexit". He said he believes he can strike a deal with the EU within weeks and was working "flat out to achieve one".
"If we can make enough progress in the next few days, I intend to go to that crucial summit... and finalise an agreement that will protect the interests of business and citizens on both sides of the channel, and on both sides of the border in Ireland," Mr Johnson said.
The prime minister had told the Mail on Sunday that the UK would break out of its "manacles" like cartoon character The Incredible Hulk, in order to leave the EU on 31 October, even without a deal.
But he told the paper a deal was possible, adding: "We will get there... I will be talking to Jean-Claude about how we're going to do it. I'm very confident."
Reports suggest Mr Johnson and his team are considering a plan to keep Northern Ireland more closely aligned to the EU after Brexit, which they hoped would remove the need for the Irish backstop - the policy in the existing withdrawal agreement to prevent a hard border returning to the island of Ireland.
This is despite the Democratic Unionist Party - which supports the Conservatives in Parliament - having rejected any plan that would see Northern Ireland treated differently to the rest of the UK.
Mr Johnson, who recently held talks with the leaders of Germany, France and Ireland, told the Mail on Sunday "there's a very, very good conversation going on about how to address the issues of the Northern Irish border".
"When I got this job everybody was saying there can be absolutely no change to the withdrawal agreement... They have already moved off that."
However, Mr Juncker told German radio on Sunday that he was not sure there was an alternative to the backstop.
He said that no "patriotic" British person would wish for a no-deal Brexit because it would leave the country in a "mess" and warned that time was running out.
And, in an update to the European Parliament last week, Mr Barnier said that while "the UK has shown a desire to intensify contacts... we will see in the coming weeks if the UK are able to give us concrete proposals in writing, which are legally operable".
