The government's final Brexit proposals will include customs checks on the island of Ireland.
The BBC's Laura Kuenssberg said Boris Johnson's plans will see Northern Ireland "in a different relationship with the EU to the rest of the UK".
Boris Johnson is addressing the Tory conference before submitting the new proposals to the EU.
The European Commission said they will "examine it objectively" and "listen carefully to the UK".
The Commission's president, Jean-Claude Juncker will talk to the PM on the phone later, while negotiating teams will meet in Brussels.
In his first speech at the event as prime minister, he will call it a "fair and reasonable" Brexit compromise, and say only by leaving the EU on 31 October can the UK "move on".
Mr Johnson will also claim the public will no longer be "taken for fools" by those who want to delay or block the process.
Tory Chairman James Cleverly said the UK had been "flexible and pragmatic", and now the EU must be the same.
On the eve of his speech, Mr Johnson told a conference fringe meeting in Manchester, hosted by the DUP, that he hoped to reach a deal with the EU over the course of "the next few days".
The government has insisted it will not negotiate a further delay beyond the Halloween deadline, saying this would be unnecessary and costly for the UK.
However, under the terms of a law passed by Parliament last month, the PM faces having to request another extension unless MPs back the terms of withdrawal by 19 October - two days after a summit of European leaders.
On Tuesday, Mr Johnson dismissed leaked reports that customs posts could be set up on either side of the border between Northern Ireland and the Republic of Ireland.
He said suggestions the UK wanted "clearance zones" for goods as part of a package of alternative arrangements to replace the Irish backstop were wide of the mark.
While he conceded some customs checks would be needed as the UK leaves the EU's customs union and single market, he said technology could keep them to an "absolute minimum".
What is in the proposals?
The issue of the Irish border - and how to keep it free from border checks when it becomes the frontier between the UK and the EU - has been a key sticking point in Brexit negotiations.
Mr Johnson says the solution reached by the EU and Theresa May, the backstop, is "anti-democratic" and "inconsistent with the sovereignty of the UK", claiming it offered no means for the UK to unilaterally exit and no say for the people of Northern Ireland over the rules that would apply there.
BBC political editor Laura Kuenssberg said the new offer from Mr Johnson included some new customs checks on the island of Ireland, and would leave Northern Ireland in a different relationship with the EU to the rest of the UK in some ways.
She said the plans were "based on the notion of consent", giving more powers to Northern Ireland's devolved Parliament - the Stormont Assembly - to shape its future relationship with the EU - despite the fact the assembly is approaching 1,000 days without sitting.
The proposals also suggest a time period for when the relationship between Northern Ireland and the EU could move on.
But the full and precise details of Mr Johnson's plan twill not be clear until after the prime minister's speech at conference.
Will the EU agree to the plans?
Speaking to BBC Radio 4's Today programme earlier, Mr Cleverly appeared to put the ball in the EU's court.
"We have been in negotiating for some while," he said. "The UK has been flexible, but a negotiation means both parties need to be flexible.
"What we need to see now is the EU be flexible - and if they can be pragmatic and flexible, we can leave with a deal on 31 October. But we are going to leave on 31 October whatever."
Irish Fine Gael senator Neale Richmond told Today that the PM's plans were a "big move" from the withdrawal agreement made by Theresa May.
Mr Richmond said, under the plan, Northern Ireland would leave the customs union and "come out of the single market in all areas, apart from agri-food products and industrial products, and indeed it only stays in those areas for four years".
This, he added, would require "additional checks" on the island of Ireland - something he described as "extremely disappointing".
Laura Kuenssberg said there was a "real expectation and belief" in No 10 that "this is now the crunch point".
She said: "This is the moment…where the EU will have to respond and say [either] there is something that is a basis of a deal here, or not.
"And what Boris Johnson is trying to suggest is if the answer is not, then for him, that means no-deal."
The EU needs to see the precise details of Boris Johnson's proposals, but the direction of travel that has been coming through is different.
The very idea of customs check between Ireland and Northern Ireland, the promise of the use of technologies to ease the process that haven't yet been tried and tested, or don't even exist yet…that is a big no-no for the EU.
The bloc will look at the proposals carefully. They need to try as they do want a deal, and also they need to be seen to be trying.
But it is fundamentally misunderstanding the EU if the prime minister thinks at this stage the 26 EU leaders will turn round on the Irish prime minister and say: "Listen, you are going to have to accept this because we just want to have a deal."
It is also fundamentally misunderstanding the German Chancellor Angela Merkel, her attachment to EU unity and the integrity of the single market.
And also it is misunderstanding that the EU sees this in a bigger picture. If suddenly now they were to back down to all of the prime minister's demands how would that look to other trade partners across the globe.
So EU leaders will be very careful not to rubbish the prime minister's ideas, to talk about them as a basis for an agreement, but if it is take it or leave it, they will be leaving at this point.
Will MPs agree?
BBC assistant political editor Norman Smith said it was particularly important Mr Johnson secured the support of the Democratic Unionist Party's 10 MPs.
He said: "I think it is very clear this deal is not going to fly unless Boris Johnson can bring the DUP along with him... one way or another he has to make sure they're on board."
BBC Northern Ireland political editor Mark Devenport said sources from the DUP were supportive of the proposals and had been kept informed during their development.
However, the party's leader, Arlene Foster, declined to say whether she had seen the PM's proposals.
She told the BBC: "What we are doing with this prime minister is working very closely with him and we will continue to work closely with him over the next couple of hours and days.
"I hope we do get a deal that is acceptable to the European Union and one that is good for the whole of the United Kingdom."
What is Mr Johnson going to say at conference?
Speaking in Manchester, Mr Johnson will suggest voters are "desperate" for the country to focus on other priorities and will contrast his determination to leave on 31 October with the "years of uncertainty" that he says would result from a Labour government promising another referendum.
"What people want, what Leavers want, what Remainers want, what the whole world wants - is to move on," he is expected to say.
"I am afraid that after three-and-a-half years people are beginning to feel that they are being taken for fools.
"They are beginning to suspect that there are forces in this country that simply don't want Brexit delivered at all.
"And if they turn out to be right in that suspicion then I believe there will be grave consequences for trust in democracy.
"Let's get Brexit done on October 31 so in 2020 our country can move on."
Mr Johnson's conference speech is set to clash with Prime Minister's Questions, which is taking place at 12.00 BST.
Normally the Commons goes into recess for the Tory conference, but MPs voted against this amid the bitter fallout from the government's unlawful prorogation of Parliament.
Foreign Secretary Dominic Raab will deputise for the prime minister, facing the shadow home secretary Diane Abbott over the despatch box.
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