Video report by ITV News Political Correspondent Carl Dinnen
The prime minister told ITV News he would present the EU with a "very good offer" to resolve the issue of the Northern Irish backstop, but said he is "not so sure they will accept".
The is the EU's insurance policy against a hard border in Ireland, which the prime minister says would effectively keep the UK inside the customs union indefinitely - it's the main sticking point in negotiations.
ITV News Political Editor Robert Peston has the latest from the Tory conference
He said reports by Irish broadcaster RTE were "inaccurate", but said the EU insists on checks being carried out on goods and services crossing the Irish border if the UK leaves the customs union.
Video report by ITV News Political Correspondent Paul Brand
He said: "What we are saying is those checks don’t need to take place at the border, they don’t need to necessitate, they don’t need to involve new infrastructure, but you must, and this where rubber hits road, but you must have checks of some kind.
"They can be checks between importer and exporter, the expediter and the recipient, there are ways of managing it that don’t involve physical infrastructure and aren’t laborious."
He added: "Suggestions that we are creating new customs checks five miles in from the new border is obviously not right."
Pressed on whether there would be any physical checks on the island of Ireland, at the border or away from it, the prime minister insisted there would not.
He told broadcasters the leaks were "confused" and claimed "they don't actually relate to what we are going to table".
He added: "One thing is clear, we don't want to see new border posts just away from the border - that's not what we're envisaging."
Watch the full interview here: