Johnson will address the Tory conference before submitting new proposals, intended to form the legal text of a new Brexit deal, to Brussels, the BBC reported.
Only by leaving the EU on October 31 can the UK "move on", he will argue.
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, 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".
Later, he will claim the public will no longer be "taken for fools" by those who want to delay or block the process.
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, Johnson faces having to request another extension unless MPs back the terms of withdrawal by October 19 - two days after a summit of European leaders.
On Tuesday, the British PM 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".
Speaking to BBC Radio 4's Today programme, 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 October 31. But we are going to leave on October 31 whatever."
( With inputs from IANS )