Boris Johnson says the “reality” of Brexit is there will need to be customs checks on the island of Ireland after the UK leaves the EU.
But the PM rejected claims that would effectively mean a hard border, in the form of a series of customs posts set five or 10 miles back.
He told BBC Radio 4’s Today programme: “A sovereign united country must have a single customs territory.”
He refused to give details, but said formal proposals would be made soon.
Government sources told the BBC on Monday night it had prepared the legal text of an updated Brexit deal and would be making more plans public in the coming days.
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.
The current government says the solution reached by the EU and Theresa May, the backstop, is unacceptable and an alternative to it must be found.
Mr Johnson was speaking at the start of the third day of the Conservative Party conference in Manchester.
The government has made a raft of policy announcements, including raising the National Living Wage over the next five years and investing into roads and bus networks.
But the plans have been overshadowed by allegations that Mr Johnson squeezed the thigh of a journalist under a table at a lunch in 1999.
Asked about the allegation by Charlotte Edwardes, the PM told Breakfast: “They’re not true. It’s obviously very sad that someone should make such allegations.”
The BBC’s Iain Watson said according to leaked proposals, the government accepts there must be customs checks on the island of Ireland, but they would be conducted away from the border.
Customs formalities would be carried out mostly where goods originate or at their final destination.
The Irish broadcaster RTE had reported that a “string of customs posts perhaps five to 10 miles away from the frontier” had been floated by the UK.
But the prime minister insisted “that’s not what we’re proposing at all”.
He would not reveal details of the proposals to be put to the EU, telling Today he “would like to veil our proposals in decent obscurity” before sharing them.
But Mr Johnson said this was the “moment the rubber hits the road” and the UK would making “a very good offer”.
He also insisted the government had made “a great deal of progress” in negotiations since August, and they were working “flat out to get a deal”.
News from BBC