The UK is not prepared to delay Brexit beyond the 31 October deadline, Boris Johnson will tell European Commission President Jean-Claude Juncker later.
The lunchtime meeting in Luxembourg will be the first time the pair have met since the PM took office in July.
Foreign Secretary Dominic Raab said the PM would stress he wanted a deal, but there had to be “some finality” to it.
But ex-minister David Gauke said there were no new detailed plans to replace the controversial Irish backstop.
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.
The Downing Street 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.”
“This is why the PM will stress to Mr Juncker that, while he wants to secure a deal, if no deal can be agreed by October 18 his policy is to leave without a deal on October 31 – and reject any delay offered by the EU.”
However, EU officials who have been involved in the Brexit talks say they have not seen the progress around the negotiating table that the UK is talking about, said the BBC’s Brussels reporter Adam Fleming.
Former justice secretary David Gauke told BBC Radio 4’s Today programme on Monday: “It still remains the case the UK government has not produced detailed proposals as to how it wants to replace the Irish backstop.
“But I very much welcome the intention of the prime minister to get a deal. But to get a deal – and I hope he does get a deal – we’ve clearly got to come forward with detailed proposals.”
But Mr Raab said claims the UK was dragging its feet were part of the “tactical posturing that goes on in any negotiation”.
He told Today that the UK had been clear the “anti-democratic backstop” had to be removed from the withdrawal current agreement and the outline of future trading relationship set out in the political declaration had to be much more ambitious.
“The EU knows our position. Lots of the detail has been talked through at technical and political level,” he said. “The framework is very clear.
“But of course the nature of these negotiations is that there will be a tendency to rubbish things we put forward in order to exact further demands. We are not going to get involved in that.”
In an interview with German radio on Sunday, Mr Juncker also said he was unsure there was an alternative to the Irish backstop.
The backstop is the controversial policy in the existing withdrawal agreement aimed at preventing a hard border returning to the island of Ireland.
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.”
The prime minister has also said he is “cautiously optimistic” a Brexit deal can be reached – but Mr Barnier said last week there were no “reasons to be optimistic”.
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.
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.”
On Sunday, Mr Juncker told German radio 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”.