The Prime Minister briefed the Cabinet on progress in the negotiations in Brussels in a conference call on Sunday, Downing Street said.
A Number 10 spokesman said: "The Prime Minister updated Cabinet on the current progress being made in ongoing Brexit negotiations, reiterating that a pathway to a deal could be seen but that there is still a significant amount of work to get there and we must remain prepared to leave 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, investing in our NHS, tackling violent crime, and dealing with the cost of living."
Mr Johnson steadfastly reiterated his pledge that he will make sure Brexit happens by the October 31 deadline.
Meanwhile, Jeremy Corbyn has signalled Labour is unlikely to back any Brexit deal struck by Boris Johnson, even if there was a confirmatory referendum.
On Saturday, shadow Brexit secretary Sir Keir Starmer said if the Prime Minister returned from Brussels with an agreement Labour would demand it was put to the country in a confirmatory vote.
However, questioned on Sky News's Sophy Ridge on Sunday programme, Mr Corbyn showed little enthusiasm for the idea.
He said: "I think many in Parliament, not necessarily Labour MPs, others, might be more inclined to support it (if there was a referendum) even if they don't really agree with the deal. I would caution them on this."
Mr Corbyn also said there was now a "strong possibility" there would be a general election before Christmas.
The PM has repeatedly called for one - though Labour has refused to back one until the possibility of a no deal Brexit is ruled out.
Mr Corbyn added his opinion that it was "ludicrous" for the Government to be holding a Queen's Speech on Monday when it was more than 40 votes short of a Commons majority.
It comes after Jacob Rees-Mogg has issued an appeal to Brexiteers to trust the PM as negotiations on a deal with Brussels enter a critical stage.
The Leader of the Commons, who was a thorn in the side of Theresa May over Brexit before joining Mr Johnson's administration, warned compromise was inevitable if there was to be an agreement.
He hinted he may even have to "eat my words" and support a plan close to one put forward by Mrs May, which he described as "completely cretinous".
Mr Rees-Mogg who previously led the strongly pro-Brexit European Research Group insisted Leave supporters could have confidence Mr Johnson would not give too much ground to Brussels in order to get a deal.
"I think that he is somebody who even the arch Eurosceptics, even a member of the Brexit Party, can trust and have confidence in," he told Sky News's Sophy Ridge on Sunday programme.
His comments will be seen as a sign of nervousness that hardline Tory Brexiteers could scupper any agreement Mr Johnson is able to reach, just as they thwarted his predecessor.
Additional reporting by PA.