The government’s final Brexit proposals will include customs checks on the island of Ireland.
Report says Boris Johnson’s plans will see Northern Ireland “in a different relationship with the EU to the rest of the UK”.
Report also said the Northern Ireland Assembly would be given powers to shape its future with the bloc.
Boris Johnson will address the Tory conference before submitting the new proposals to 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”.
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.
Report says 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.
It was reported that 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 will not be clear until after the prime minister’s speech at conference.
According to reports, 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 said 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”.
Report says there was a “real expectation and belief” in No 10 that “this is now the crunch point”.
“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.”