Mr Johnson will then write to the European Union requesting a Brexit delay if Parliament does not approve a deal on Saturday.
Parliament will meet next Saturday to vote on any deal achieved by the PM at a Brussels summit this week. "We remain prepared to leave without a deal on October 31".
British Prime Minister Boris Johnson told Cabinet colleagues that it will require a "significant amount of work" to strike a Brexit deal with the European Union, amid signs of progress in last-minute talks but also deep-seated skepticism about the chances of an agreement.
The prime minister is hoping to hurry by means of Parliament a Withdrawal Settlement Invoice to ratify any deal he manages to strike at this week's European Union summit, in time for Britain to depart on 31 October, as he has lengthy promised. "But if Boris Johnson were to ask for extra time - which probably he won't - I would consider it unhistoric to refuse such a request".
Earlier, Johnson briefed cabinet members on progress in those talks by conference call. "We remain prepared to leave without a deal on October 31".
"The Prime Minister said there was a way forward for a deal that could secure all our interests, respect the Good Friday Agreement, get rid of the backstop and get Brexit done by October 31 so we can push on with domestic agenda", a No 10 spokesperson said.
"His latest move shows that he is not trying to stop no-deal - he is trying to enforce a no Brexit'".
The government says it is doing everything it can to get a deal, and that it has contingency plans to mitigate the impact of a no-deal exit.
It's similar to a "customs partnership" plan the European Union rejected in 2018, and would leave Northern Ireland with a different customs regime to the rest of the U.K. British authorities would have to collect tariffs on behalf of the bloc on goods crossing the Irish Sea.
Johnson will offer the three leaders the option to either help him deliver a new deal this week, or to agree on a friendly version of a no-deal Brexit by October 31, the newspaper said, citing a source familiar with the conversations.
Other options reviewed by pro-Remain MPs include reviving Theresa May's deal, which was rejected the three times by the Parliament, and making it subject to a second referendum.
That leaves Johnson's hopes pinned to a group of Labour rebels and the small party which notionally keeps him in power, Northern Ireland's Democratic Unionist Party.
The British and Irish governments' plan to break the impasse suffered an apparent setback after the DUP's Nigel Dodds said the double customs solution "cannot work", and Brexiteer Owen Paterson, a former Northern Ireland secretary, suggested it would "ride roughshod" over the Good Friday Agreement.